DF-QSM: Data Fidelity based Hybrid Approach for Improved Quantitative Susceptibility Mapping of the Brain

Quantitative Susceptibility Mapping (QSM) is an advanced magnetic resonance imaging (MRI) technique to quantify the magnetic susceptibility of the tissue under investigation. Deep learning methods have shown promising results in deconvolving the susceptibility distribution from the measured local field obtained from the MR phase. Although existing deep learning based QSM methods can produce high-quality reconstruction, they are highly biased toward training data distribution with less scope for generalizability. This work proposes a hybrid two-step reconstruction approach to improve deep learning based QSM reconstruction. The susceptibility map prediction obtained from the deep learning methods has been refined in the framework developed in this work to ensure consistency with the measured local field. The developed method was validated on existing deep learning and model-based deep learning methods for susceptibility mapping of the brain. The developed method resulted in improved reconstruction for MRI volumes obtained with different acquisition settings, including deep learning models trained on constrained (limited) data settings.

Spinet-QSM: model-based deep learning with schatten p-norm regularization for improved quantitative susceptibility mapping

OBJECTIVE

Quantitative susceptibility mapping (QSM) provides an estimate of the magnetic susceptibility of tissue using magnetic resonance (MR) phase measurements. The tissue magnetic susceptibility (source) from the measured magnetic field distribution/local tissue field (effect) inherent in the MR phase images is estimated by numerically solving the inverse source-effect problem. This study aims to develop an effective model-based deep-learning framework to solve the inverse problem of QSM.

MATERIALS AND METHODS

This work proposes a Schatten p -norm-driven model-based deep learning framework for QSM with a learnable norm parameter p to adapt to the data. In contrast to other model-based architectures that enforce the l2 -norm or l1 -norm for the denoiser, the proposed approach can enforce any p -norm ( 0 < p ≤ 2 ) on a trainable regulariser.

RESULTS

The proposed method was compared with deep learning-based approaches, such as QSMnet, and model-based deep learning approaches, such as learned proximal convolutional neural network (LPCNN). Reconstructions performed using 77 imaging volumes with different acquisition protocols and clinical conditions, such as hemorrhage and multiple sclerosis, showed that the proposed approach outperformed existing state-of-the-art methods by a significant margin in terms of quantitative merits.

CONCLUSION

The proposed SpiNet-QSM showed a consistent improvement of at least 5% in terms of the high-frequency error norm (HFEN) and normalized root mean squared error (NRMSE) over other QSM reconstruction methods with limited training data.

Fully automated sinogram-based deep learning model for detection and classification of intracranial hemorrhage

PURPOSE

To propose an automated approach for detecting and classifying Intracranial Hemorrhages (ICH) directly from sinograms using a deep learning framework. This method is proposed to overcome the limitations of the conventional diagnosis by eliminating the time-consuming reconstruction step and minimizing the potential noise and artifacts that can occur during the Computed Tomography (CT) reconstruction process.

METHODS

This study proposes a two-stage automated approach for detecting and classifying ICH from sinograms using a deep learning framework. The first stage of the framework is Intensity Transformed Sinogram Sythesizer, which synthesizes sinograms that are equivalent to the intensity-transformed CT images. The second stage comprises of a cascaded Convolutional Neural Network-Recurrent Neural Network (CNN-RNN) model that detects and classifies hemorrhages from the synthesized sinograms. The CNN module extracts high-level features from each input sinogram, while the RNN module provides spatial correlation of the neighborhood regions in the sinograms. The proposed method was evaluated on a publicly available RSNA dataset consisting of a large sample size of 8652 patients.

RESULTS

The results showed that the proposed method had a notable improvement as high as 27% in patient-wise accuracies when compared to state-of-the-art methods like ResNext-101, Inception-v3 and Vision Transformer. Furthermore, the sinogram-based approach was found to be more robust to noise and offset errors in comparison to CT image-based approaches. The proposed model was also subjected to a multi-label classification analysis to determine the hemorrhage type from a given sinogram. The learning patterns of the proposed model were also examined for explainability using the activation maps.

CONCLUSION

The proposed sinogram-based approach can provide an accurate and efficient diagnosis of ICH without the need for the time-consuming reconstruction step and can potentially overcome the limitations of CT image-based approaches. The results show promising outcomes for the use of sinogram-based approaches in detecting hemorrhages, and further research can explore the potential of this approach in clinical settings.

Model resolution-based deconvolution for improved quantitative susceptibility mapping

Quantitative susceptibility mapping (QSM) utilizes the relationship between the measured local field and the unknown susceptibility map to perform dipole deconvolution. The aim of this work is to introduce and systematically evaluate the model resolution-based deconvolution for improved estimation of the susceptibility map obtained using the thresholded k-space division (TKD). A two-step approach has been proposed, wherein the first step involves the TKD susceptibility map computation and the second step involves the correction of this susceptibility map using the model-resolution matrix. The TKD-estimated susceptibility map can be expressed as the weighted average of the true susceptibility map, where the weights are determined by the rows of the model-resolution matrix, and hence a deconvolution of the TKD susceptibility map using the model-resolution matrix yields a better approximation to the true susceptibility map. The model resolution-based deconvolution is realized using closed-form, iterative, and sparsity-regularized implementations. The proposed approach was compared with L2 regularization, TKD, rescaled TKD in superfast dipole inversion, the modulated closed-form method, and iterative dipole inversion, as well as sparsity-regularized dipole inversion. It was observed that the proposed approach showed a substantial reduction in the streaking artifacts across 94 test volumes considered in this study. The proposed approach also showed better error reduction and edge preservation compared with other approaches. The proposed model resolution-based deconvolution compensates for the truncation of zero coefficients in the dipole kernel at the magic angle and hence provides a closer approximation to the true susceptibility map compared with other direct methods.

Transformer-Based Automated Segmentation of the Median Nerve in Ultrasound Videos of Wrist-to-Elbow Region

Segmenting the median nerve is essential for identifying nerve entrapment syndromes, guiding surgical planning and interventions, and furthering understanding of nerve anatomy. This study aims to develop an automated tool that can assist clinicians in localizing and segmenting the median nerve from the wrist, mid-forearm, and elbow in ultrasound videos. This is the first fully automated single deep learning model for accurate segmentation of the median nerve from the wrist to the elbow in ultrasound videos, along with the computation of the cross-sectional area (CSA) of the nerve. The visual transformer architecture, which was originally proposed to detect and classify 41 classes in YouTube videos, was modified to predict the median nerve in every frame of ultrasound videos. This is achieved by modifying the bounding box sequence matching block of the visual transformer. The median nerve segmentation is a binary class prediction, and the entire bipartite matching sequence is eliminated, enabling a direct comparison of the prediction with expert annotation in a frame-by-frame fashion. Model training, validation, and testing were performed on a dataset comprising ultrasound videos collected from 100 subjects, which were partitioned into 80, ten, and ten subjects, respectively. The proposed model was compared with U-Net, U-Net++, Siam U-Net, Attention U-Net, LSTM U-Net, and Trans U-Net. The proposed transformer-based model effectively leveraged the temporal and spatial information present in ultrasound video frames and efficiently segmented the median nerve with an average dice similarity coefficient (DSC) of approximately 94% at the wrist and 84% in the entire forearm region.

Siamese-SR: A Siamese Super-Resolution Model for Boosting Resolution of Digital Rock Images for Improved Petrophysical Property Estimation

Digital Rock Physics leverages advances in digital image acquisition and analysis techniques to create 3D digital images of rock samples, which are used for computational modeling and simulations to predict petrophysical properties of interest. However, the accuracy of the predictions is crucially dependent on the quality of the digital images, which is currently limited by the resolution of the micro-CT scanning technology. We have proposed a novel Deep Learning based Super-Resolution model called Siamese-SR to digitally boost the resolution of Digital Rock images whilst retaining the texture and providing optimal de-noising. The Siamese-SR model consists of a generator which is adversarially trained with a relativistic and a siamese discriminator utilizing Materials In Context (MINC) loss estimator. This model has been demonstrated to improve the resolution of sandstone rock images acquired using micro-CT scanning by a factor of 2. Another key highlight of our work is that for the evaluation of the super-resolution performance, we propose to move away from image-based metrics such as Structural Similarity (SSIM) and Peak Signal to Noise Ratio (PSNR) because they do not correlate well with expert geological and petrophysical evaluations. Instead, we propose to subject the super-resolved images to the next step in the Digital Rock workflow to calculate a crucial petrophysical property of interest, viz. porosity and use it as a metric for evaluation of our proposed Siamese-SR model against several other existing super-resolution methods like SRGAN, ESRGAN, EDSR and SPSR. Furthermore, we also use Local Attribution Maps to show how our proposed Siamese-SR model focuses optimally on edge-semantics, which is what leads to improvement in the image-based porosity prediction, the permeability prediction from Multiple Relaxation Time Lattice Boltzmann Method (MRTLBM) flow simulations as well as the prediction of other petrophysical properties of interest derived from Mercury Injection Capillary Pressure (MICP) simulations.

Multi GPU parallelization of maximum likelihood expectation maximization method for digital rock tomography data

Digital rock is an emerging area of rock physics, which involves scanning reservoir rocks using X-ray micro computed tomography (XCT) scanners and using it for various petrophysical computations and evaluations. The acquired micro CT projections are used to reconstruct the X-ray attenuation maps of the rock. The image reconstruction problem can be solved by utilization of analytical (such as Feldkamp–Davis–Kress (FDK) algorithm) or iterative methods. Analytical schemes are typically computationally more efficient and hence preferred for large datasets such as digital rocks. Iterative schemes like maximum likelihood expectation maximization (MLEM) are known to generate accurate image representation over analytical scheme in limited data (and/or noisy) situations, however iterative schemes are computationally expensive. In this work, we have parallelized the forward and inverse operators used in the MLEM algorithm on multiple graphics processing units (multi-GPU) platforms. The multi-GPU implementation involves dividing the rock volumes and detector geometry into smaller modules (along with overlap regions). Each of the module was passed onto different GPU to enable computation of forward and inverse operations. We observed an acceleration of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 30$$\end{document}∼30 times using our multi-GPU approach compared to the multi-core CPU implementation. Further multi-GPU based MLEM obtained superior reconstruction compared to traditional FDK algorithm.

Binary photoacoustic tomography for improved vasculature imaging

SIGNIFICANCE

The proposed binary tomography approach was able to recover the vasculature structures accurately, which could potentially enable the utilization of binary tomography algorithm in scenarios such as therapy monitoring and hemorrhage detection in different organs.

AIM

Photoacoustic tomography (PAT) involves reconstruction of vascular networks having direct implications in cancer research, cardiovascular studies, and neuroimaging. Various methods have been proposed for recovering vascular networks in photoacoustic imaging; however, most methods are two-step (image reconstruction and image segmentation) in nature. We propose a binary PAT approach wherein direct reconstruction of vascular network from the acquired photoacoustic sinogram data is plausible.

APPROACH

Binary tomography approach relies on solving a dual-optimization problem to reconstruct images with every pixel resulting in a binary outcome (i.e., either background or the absorber). Further, the binary tomography approach was compared against backprojection, Tikhonov regularization, and sparse recovery-based schemes.

RESULTS

Numerical simulations, physical phantom experiment, and in-vivo rat brain vasculature data were used to compare the performance of different algorithms. The results indicate that the binary tomography approach improved the vasculature recovery by 10% using in-silico data with respect to the Dice similarity coefficient against the other reconstruction methods.

CONCLUSION

The proposed algorithm demonstrates superior vasculature recovery with limited data both visually and based on quantitative image metrics.

Mini-COVIDNet: Efficient Lightweight Deep Neural Network for Ultrasound Based Point-of-Care Detection of COVID-19

Lung ultrasound (US) imaging has the potential to be an effective point-of-care test for detection of COVID-19, due to its ease of operation with minimal personal protection equipment along with easy disinfection. The current state-of-the-art deep learning models for detection of COVID-19 are heavy models that may not be easy to deploy in commonly utilized mobile platforms in point-of-care testing. In this work, we develop a lightweight mobile friendly efficient deep learning model for detection of COVID-19 using lung US images. Three different classes including COVID-19, pneumonia, and healthy were included in this task. The developed network, named as Mini-COVIDNet, was bench-marked with other lightweight neural network models along with state-of-the-art heavy model. It was shown that the proposed network can achieve the highest accuracy of 83.2% and requires a training time of only 24 min. The proposed Mini-COVIDNet has 4.39 times less number of parameters in the network compared to its next best performing network and requires a memory of only 51.29 MB, making the point-of-care detection of COVID-19 using lung US imaging plausible on a mobile platform. Deployment of these lightweight networks on embedded platforms shows that the proposed Mini-COVIDNet is highly versatile and provides optimal performance in terms of being accurate as well as having latency in the same order as other lightweight networks. The developed lightweight models are available at https://github.com/navchetan-awasthi/Mini-COVIDNet.

Dimensionality reduced plug and play priors for improving photoacoustic tomographic imaging with limited noisy data

The reconstruction methods for solving the ill-posed inverse problem of photoacoustic tomography with limited noisy data are iterative in nature to provide accurate solutions. These methods performance is highly affected by the noise level in the photoacoustic data. A singular value decomposition (SVD) based plug and play priors method for solving photoacoustic inverse problem was proposed in this work to provide robustness to noise in the data. The method was shown to be superior as compared to total variation regularization, basis pursuit deconvolution and Lanczos Tikhonov based regularization and provided improved performance in case of noisy data. The numerical and experimental cases show that the improvement can be as high as 8.1 dB in signal to noise ratio of the reconstructed image and 67.98% in root mean square error in comparison to the state of the art methods.

Anam-Net: Anamorphic Depth Embedding-Based Lightweight CNN for Segmentation of Anomalies in COVID-19 Chest CT Images

Chest computed tomography (CT) imaging has become indispensable for staging and managing coronavirus disease 2019 (COVID-19), and current evaluation of anomalies/abnormalities associated with COVID-19 has been performed majorly by the visual score. The development of automated methods for quantifying COVID-19 abnormalities in these CT images is invaluable to clinicians. The hallmark of COVID-19 in chest CT images is the presence of ground-glass opacities in the lung region, which are tedious to segment manually. We propose anamorphic depth embedding-based lightweight CNN, called Anam-Net, to segment anomalies in COVID-19 chest CT images. The proposed Anam-Net has 7.8 times fewer parameters compared to the state-of-the-art UNet (or its variants), making it lightweight capable of providing inferences in mobile or resource constraint (point-of-care) platforms. The results from chest CT images (test cases) across different experiments showed that the proposed method could provide good Dice similarity scores for abnormal and normal regions in the lung. We have benchmarked Anam-Net with other state-of-the-art architectures, such as ENet, LEDNet, UNet++, SegNet, Attention UNet, and DeepLabV3+. The proposed Anam-Net was also deployed on embedded systems, such as Raspberry Pi 4, NVIDIA Jetson Xavier, and mobile-based Android application (CovSeg) embedded with Anam-Net to demonstrate its suitability for point-of-care platforms. The generated codes, models, and the mobile application are available for enthusiastic users at https://github.com/NaveenPaluru/Segmentation-COVID-19.

Non-local means improves total-variation constrained photoacoustic image reconstruction

Photoacoustic/Optoacoustic tomography aims to reconstruct maps of the initial pressure rise induced by the absorption of light pulses in tissue. This reconstruction is an ill-conditioned and under-determined problem, when the data acquisition protocol involves limited detection positions. The aim of the work is to develop an inversion method which integrates denoising procedure within the iterative model-based reconstruction to improve quantitative performance of optoacoustic imaging. Among the model-based schemes, total-variation (TV) constrained reconstruction scheme is a popular approach. In this work, a two-step approach was proposed for improving the TV constrained optoacoustic inversion by adding a non-local means based filtering step within each TV iteration. Compared to TV-based reconstruction, inclusion of this non-local means step resulted in signal-to-noise ratio improvement of 2.5 dB in the reconstructed optoacoustic images.

Deep Neural Network-Based Sinogram Super-Resolution and Bandwidth Enhancement for Limited-Data Photoacoustic Tomography

Photoacoustic tomography (PAT) is a noninvasive imaging modality combining the benefits of optical contrast at ultrasonic resolution. Analytical reconstruction algorithms for photoacoustic (PA) signals require a large number of data points for accurate image reconstruction. However, in practical scenarios, data are collected using the limited number of transducers along with data being often corrupted with noise resulting in only qualitative images. Furthermore, the collected boundary data are band-limited due to limited bandwidth (BW) of the transducer, making the PA imaging with limited data being qualitative. In this work, a deep neural network-based model with loss function being scaled root-mean-squared error was proposed for super-resolution, denoising, as well as BW enhancement of the PA signals collected at the boundary of the domain. The proposed network has been compared with traditional as well as other popular deep-learning methods in numerical as well as experimental cases and is shown to improve the collected boundary data, in turn, providing superior quality reconstructed PA image. The improvement obtained in the Pearson correlation, structural similarity index metric, and root-mean-square error was as high as 35.62%, 33.81%, and 41.07%, respectively, for phantom cases and signal-to-noise ratio improvement in the reconstructed PA images was as high as 11.65 dB for in vivo cases compared with reconstructed image obtained using original limited BW data. Code is available at https://sites.google.com/site/sercmig/home/dnnpat.

Guided filter based image enhancement for focal error compensation in low cost automated histopathology microscopic system

Low-cost automated histopathology microscopy systems usually suffer from optical imperfections, producing images that are slightly Out of Focus (OoF). In this work, a guided filter (GF) based image preprocessing is proposed for compensating focal errors and its efficacy is demonstrated on images of healthy and malaria infected red blood cells (h-RBCs and i-RBCs), and PAP smears. Since contrast enhancement has been widely used as an image preprocessing step for the analysis of histopathology images, a systematic comparison is made with six such prominently used methods, namely Contrast Limited Adaptive Histogram Equalization (CLAHE), RIQMC-based optimal histogram matching (ROHIM), modified L₀, Morphological Varying(MV)-Bitonic filter, unsharp mask filter and joint bilateral filter. The images enhanced using GF approach lead to better segmentation accuracy (upto 50% improvement over native images) and visual quality compared to other approaches, without any change in the color tones. Thus, the proposed GF approach is a viable solution for rectifying the OoF microscopy images without the loss of the valuable diagnostic information presented by the color tone.

Fractional Regularization to Improve Photoacoustic Tomographic Image Reconstruction

Photoacoustic tomography involves reconstructing the initial pressure rise distribution from the measured acoustic boundary data. The recovery of the initial pressure rise distribution tends to be an ill-posed problem in the presence of noise and when limited independent data is available, necessitating regularization. The standard regularization schemes include Tikhonov, l₁ -norm, and total-variation. These regularization schemes weigh the singular values equally irrespective of the noise level present in the data. This paper introduces a fractional framework to weigh the singular values with respect to a fractional power. This fractional framework was implemented for Tikhonov, l₁ -norm, and total-variation regularization schemes. Moreover, an automated method for choosing the fractional power was also proposed. It was shown theoretically and with numerical experiments that the fractional power is inversely related to the data noise level for fractional Tikhonov scheme. The fractional framework outperforms the standard regularization schemes, Tikhonov, l₁ -norm, and total-variation by 54% in numerical simulations, experimental phantoms, and in vivo rat data in terms of observed contrast/signal-to-noise-ratio of the reconstructed images.

PA-Fuse: deep supervised approach for the fusion of photoacoustic images with distinct reconstruction characteristics

The methods available for solving the inverse problem of photoacoustic tomography promote only one feature-either being smooth or sharp-in the resultant image. The fusion of photoacoustic images reconstructed from distinct methods improves the individually reconstructed images, with the guided filter based approach being state-of-the-art, which requires that implicit regularization parameters are chosen. In this work, a deep fusion method based on convolutional neural networks has been proposed as an alternative to the guided filter based approach. It has the combined benefit of using less data for training without the need for the careful choice of any parameters and is a fully data-driven approach. The proposed deep fusion approach outperformed the contemporary fusion method, which was proved using experimental, numerical phantoms and in-vivo studies. The improvement obtained in the reconstructed images was as high as 95.49% in root mean square error and 7.77 dB in signal to noise ratio (SNR) in comparison to the guided filter approach. Also, it was demonstrated that the proposed deep fuse approach, trained on only blood vessel type images at measurement data SNR being 40 dB, was able to provide a generalization that can work across various noise levels in the measurement data, experimental set-ups as well as imaging objects.

Spatially variant regularization based on model resolution and fidelity embedding characteristics improves photoacoustic tomography

Photoacoustic tomography tends to be an ill-conditioned problem with noisy limited data requiring imposition of regularization constraints, such as standard Tikhonov (ST) or total variation (TV), to reconstruct meaningful initial pressure rise distribution from the tomographic acoustic measurements acquired at the boundary of the tissue. However, these regularization schemes do not account for nonuniform sensitivity arising due to limited detector placement at the boundary of tissue as well as other system parameters. For the first time, two regularization schemes were developed within the Tikhonov framework to address these issues in photoacoustic imaging. The model resolution, based on spatially varying regularization, and fidelity-embedded regularization, based on orthogonality between the columns of system matrix, were introduced. These were systematically evaluated with the help of numerical and in-vivo mice data. It was shown that the performance of the proposed spatially varying regularization schemes were superior (with at least 2 dB or 1.58 times improvement in the signal-to-noise ratio) compared to ST-/TV-based regularization schemes.

Image-guided filtering for improving photoacoustic tomographic image reconstruction

Several algorithms exist to solve the photoacoustic image reconstruction problem depending on the expected reconstructed image features. These reconstruction algorithms promote typically one feature, such as being smooth or sharp, in the output image. Combining these features using a guided filtering approach was attempted in this work, which requires an input and guiding image. This approach act as a postprocessing step to improve commonly used Tikhonov or total variational regularization method. The result obtained from linear backprojection was used as a guiding image to improve these results. Using both numerical and experimental phantom cases, it was shown that the proposed guided filtering approach was able to improve (as high as 11.23 dB) the signal-to-noise ratio of the reconstructed images with the added advantage being computationally efficient. This approach was compared with state-of-the-art basis pursuit deconvolution as well as standard denoising methods and shown to outperform them.

Accelerated image reconstruction using extrapolated Tikhonov filtering for photoacoustic tomography

PURPOSE

Development of simple and computationally efficient extrapolated Tikhonov filtering reconstruction methods for photoacoustic tomography.

METHODS

The model-based reconstruction algorithms in photoacoustic tomography typically utilize Tikhonov regularization scheme for the reconstruction of initial pressure distribution from the measured boundary acoustic data. The automated choice of regularization parameter in these cases is computationally expensive. Moreover, the Tikhonov scheme promotes the smooth features in the reconstructed image due to the smooth regularizer, thus leading to loss of sharp features. The proposed extrapolation method estimates the solution at zero regularization assuming the solution being a function of regularization parameter and thus posing it as a zero value problem. Thus, the numerically computed zero regularization solution is expected to have better features compared to standard Tikhonov solution, with an added advantage of removing the necessity of automated choice of regularization. The reconstructed results using this method were shown in three variants (Lanczos, traditional, and exponential) of Tikhonov filtering and were compared with the standard error estimate technique.

RESULTS

Four numerical (including realistic breast phantom) and two experimental phantom data were utilized to show the effectiveness of the proposed method. It was shown that the proposed method performance was superior than the standard error estimate technique, being at least four times faster in terms of computation, and provides an improvement as high as 2.6 times in terms of standard figures of merit.

CONCLUSION

The developed extrapolated Tikhonov filtering methods overcome the difficulty of obtaining a suitable regularization parameter and shown to be reconstructing high-quality photoacoustic images with additional advantage of being computationally efficient, making it more appealing in real-time applications.

Vector extrapolation methods for accelerating iterative reconstruction methods in limited-data photoacoustic tomography

As limited data photoacoustic tomographic image reconstruction problem is known to be ill-posed, the iterative reconstruction methods were proven to be effective in terms of providing good quality initial pressure distribution. Often, these iterative methods require a large number of iterations to converge to a solution, in turn making the image reconstruction procedure computationally inefficient. In this work, two variants of vector polynomial extrapolation techniques were deployed to accelerate two standard iterative photoacoustic image reconstruction algorithms, including regularized steepest descent and total variation regularization methods. It is shown using numerical and experimental phantom cases that these extrapolation methods that are proposed in this work can provide significant acceleration (as high as 4.7 times) along with added advantage of improving reconstructed image quality.

Deep neural network-based bandwidth enhancement of photoacoustic data

Photoacoustic (PA) signals collected at the boundary of tissue are always band-limited. A deep neural network was proposed to enhance the bandwidth (BW) of the detected PA signal, thereby improving the quantitative accuracy of the reconstructed PA images. A least square-based deconvolution method that utilizes the Tikhonov regularization framework was used for comparison with the proposed network. The proposed method was evaluated using both numerical and experimental data. The results indicate that the proposed method was capable of enhancing the BW of the detected PA signal, which inturn improves the contrast recovery and quality of reconstructed PA images without adding any significant computational burden.

Population differences in brain morphology: Need for population specific brain template

Brain templates provide a standard anatomical platform for population based morphometric assessments. Typically, standard brain templates for such assessments are created using Caucasian brains, which may not be ideal to analyze brains from other ethnicities. To effectively demonstrate this, we compared brain morphometric differences between T1 weighted structural MRI images of 27 healthy Indian and Caucasian subjects of similar age and same sex ratio. Furthermore, a population specific brain template was created from MRI images of healthy Indian subjects and compared with standard Montreal Neurological Institute (MNI-152) template. We also examined the accuracy of registration of by acquiring a different T1 weighted MRI data set and registering them to newly created Indian template and MNI-152 template. The statistical analysis indicates significant difference in global brain measures and regional brain structures of Indian and Caucasian subjects. Specifically, the global brain measurements of the Indian brain template were smaller than that of the MNI template. Also, Indian brain images were better realigned to the newly created template than to the MNI-152 template. The notable variations in Indian and Caucasian brains convey the need to build a population specific Indian brain template and atlas.

Fast analytical spectral filtering methods for magnetic resonance perfusion quantification

The deconvolution in the perfusion weighted imaging (PWI) plays an important role in quantifying the MR perfusion parameters. The PWI application to stroke and brain tumor studies has become a standard clinical practice. The standard approach for this deconvolution is oscillatory-limited singular value decomposition (oSVD) and frequency domain deconvolution (FDD). The FDD is widely recognized as the fastest approach currently available for deconvolution of MR perfusion data. In this work, two fast deconvolution methods (namely analytical fourier filtering and analytical showalter spectral filtering) are proposed. Through systematic evaluation, the proposed methods are shown to be computationally efficient and quantitatively accurate compared to FDD and oSVD.

Computationally efficient error estimate for evaluation of regularization in photoacoustic tomography

The model-based image reconstruction techniques for photoacoustic (PA) tomography require an explicit regularization. An error estimate (?2) minimization-based approach was proposed and developed for the determination of a regularization parameter for PA imaging. The regularization was used within Lanczos bidiagonalization framework, which provides the advantage of dimensionality reduction for a large system of equations. It was shown that the proposed method is computationally faster than the state-of-the-art techniques and provides similar performance in terms of quantitative accuracy in reconstructed images. It was also shown that the error estimate (?2) can also be utilized in determining a suitable regularization parameter for other popular techniques such as Tikhonov, exponential, and nonsmooth (?1 and total variation norm based) regularization methods.

Exponential filtering of singular values improves photoacoustic image reconstruction

Model-based image reconstruction techniques yield better quantitative accuracy in photoacoustic image reconstruction. In this work, an exponential filtering of singular values was proposed for carrying out the image reconstruction in photoacoustic tomography. The results were compared with widely popular Tikhonov regularization, time reversal, and the state of the art least-squares QR-based reconstruction algorithms for three digital phantom cases with varying signal-to-noise ratios of data. It was shown that exponential filtering provides superior photoacoustic images of better quantitative accuracy. Moreover, the proposed filtering approach was observed to be less biased toward the regularization parameter and did not come with any additional computational burden as it was implemented within the Tikhonov filtering framework. It was also shown that the standard Tikhonov filtering becomes an approximation to the proposed exponential filtering.

Generalized Beer-Lambert model for near-infrared light propagation in thick biological tissues

The attenuation of near-infrared (NIR) light intensity as it propagates in a turbid medium like biological tissue is described by modified the Beer–Lambert law (MBLL). The MBLL is generally used to quantify the changes in tissue chromophore concentrations for NIR spectroscopic data analysis. Even though MBLL is effective in terms of providing qualitative comparison, it suffers from its applicability across tissue types and tissue dimensions. In this work, we introduce Lambert-W function-based modeling for light propagation in biological tissues, which is a generalized version of the Beer–Lambert model. The proposed modeling provides parametrization of tissue properties, which includes two attenuation coefficients μ0 and η. We validated our model against the Monte Carlo simulation, which is the gold standard for modeling NIR light propagation in biological tissue. We included numerous human and animal tissues to validate the proposed empirical model, including an inhomogeneous adult human head model. The proposed model, which has a closed form (analytical), is first of its kind in providing accurate modeling of NIR light propagation in biological tissues.

Prior image based temporally constrained reconstruction algorithm for magnetic resonance guided high intensity focused ultrasound

PURPOSE

A prior image based temporally constrained reconstruction (PITCR) algorithm was developed for obtaining accurate temperature maps having better volume coverage, and spatial, and temporal resolution than other algorithms for highly undersampled data in magnetic resonance (MR) thermometry.

METHODS

The proposed PITCR approach is an algorithm that gives weight to the prior image and performs accurate reconstruction in a dynamic imaging environment. The PITCR method is compared with the temporally constrained reconstruction (TCR) algorithm using pork muscle data.

RESULTS

The PITCR method provides superior performance compared to the TCR approach with highly undersampled data. The proposed approach is computationally expensive compared to the TCR approach, but this could be overcome by the advantage of reconstructing with fewer measurements. In the case of reconstruction of temperature maps from 16% of fully sampled data, the PITCR approach was 1.57× slower compared to the TCR approach, while the root mean square error using PITCR is 0.784 compared to 2.815 with the TCR scheme.

CONCLUSIONS

The PITCR approach is able to perform more accurate reconstructions of temperature maps compared to the TCR approach with highly undersampled data in MR guided high intensity focused ultrasound.

Basis pursuit deconvolution for improving model-based reconstructed images in photoacoustic tomography

The model-based image reconstruction approaches in photoacoustic tomography have a distinct advantage compared to traditional analytical methods for cases where limited data is available. These methods typically deploy Tikhonov based regularization scheme to reconstruct the initial pressure from the boundary acoustic data. The model-resolution for these cases represents the blur induced by the regularization scheme. A method that utilizes this blurring model and performs the basis pursuit deconvolution to improve the quantitative accuracy of the reconstructed photoacoustic image is proposed and shown to be superior compared to other traditional methods via three numerical experiments. Moreover, this deconvolution including the building of an approximate blur matrix is achieved via the Lanczos bidagonalization (least-squares QR) making this approach attractive in real-time.

Model-resolution-based basis pursuit deconvolution improves diffuse optical tomographic imaging

The image reconstruction problem encountered in diffuse optical tomographic imaging is ill-posed in nature, necessitating the usage of regularization to result in stable solutions. This regularization also results in loss of resolution in the reconstructed images. A frame work, that is attributed by model-resolution, to improve the reconstructed image characteristics using the basis pursuit deconvolution method is proposed here. The proposed method performs this deconvolution as an additional step in the image reconstruction scheme. It is shown, both in numerical and experimental gelatin phantom cases, that the proposed method yields better recovery of the target shapes compared to traditional method, without the loss of quantitativeness of the results.

Performance evaluation of typical approximation algorithms for nonconvex ℓp-minimization in diffuse optical tomography

The sparse estimation methods that utilize the ℓp-norm, with p being between 0 and 1, have shown better utility in providing optimal solutions to the inverse problem in diffuse optical tomography. These ℓp-norm-based regularizations make the optimization function nonconvex, and algorithms that implement ℓp-norm minimization utilize approximations to the original ℓp-norm function. In this work, three such typical methods for implementing the ℓp-norm were considered, namely, iteratively reweighted ℓ1-minimization (IRL1), iteratively reweighted least squares (IRLS), and the iteratively thresholding method (ITM). These methods were deployed for performing diffuse optical tomographic image reconstruction, and a systematic comparison with the help of three numerical and gelatin phantom cases was executed. The results indicate that these three methods in the implementation of ℓp-minimization yields similar results, with IRL1 fairing marginally in cases considered here in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images.

Incoherence-based optimal selection of independent measurements in diffuse optical tomography

An optimal measurement selection strategy based on incoherence among rows (corresponding to measurements) of the sensitivity (or weight) matrix for the near infrared diffuse optical tomography is proposed. As incoherence among the measurements can be seen as providing maximum independent information into the estimation of optical properties, this provides high level of optimization required for knowing the independency of a particular measurement on its counterparts. The proposed method was compared with the recently established data-resolution matrix-based approach for optimal choice of independent measurements and shown, using simulated and experimental gelatin phantom data sets, to be superior as it does not require an optimal regularization parameter for providing the same information.

A LSQR-type method provides a computationally efficient automated optimal choice of regularization parameter in diffuse optical tomography

PURPOSE

Developing a computationally efficient automated method for the optimal choice of regularization parameter in diffuse optical tomography.

METHODS

The least-squares QR (LSQR)-type method that uses Lanczos bidiagonalization is known to be computationally efficient in performing the reconstruction procedure in diffuse optical tomography. The same is effectively deployed via an optimization procedure that uses the simplex method to find the optimal regularization parameter. The proposed LSQR-type method is compared with the traditional methods such as L-curve, generalized cross-validation (GCV), and recently proposed minimal residual method (MRM)-based choice of regularization parameter using numerical and experimental phantom data.

RESULTS

The results indicate that the proposed LSQR-type and MRM-based methods performance in terms of reconstructed image quality is similar and superior compared to L-curve and GCV-based methods. The proposed method computational complexity is at least five times lower compared to MRM-based method, making it an optimal technique.

CONCLUSIONS

The LSQR-type method was able to overcome the inherent limitation of computationally expensive nature of MRM-based automated way finding the optimal regularization parameter in diffuse optical tomographic imaging, making this method more suitable to be deployed in real-time.

Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography

A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison.

Nonquadratic penalization improves near-infrared diffuse optical tomography

A new approach that can easily incorporate any generic penalty function into the diffuse optical tomographic image reconstruction is introduced to show the utility of nonquadratic penalty functions. The penalty functions that were used include quadratic (ℓ2), absolute (ℓ1), Cauchy, and Geman-McClure. The regularization parameter in each of these cases was obtained automatically by using the generalized cross-validation method. The reconstruction results were systematically compared with each other via utilization of quantitative metrics, such as relative error and Pearson correlation. The reconstruction results indicate that, while the quadratic penalty may be able to provide better separation between two closely spaced targets, its contrast recovery capability is limited, and the sparseness promoting penalties, such as ℓ1, Cauchy, and Geman-McClure have better utility in reconstructing high-contrast and complex-shaped targets, with the Geman-McClure penalty being the most optimal one.

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part II: comparison and validation

The analytical solutions for the coupled diffusion equations that are encountered in diffuse fluorescence spectroscopy/imaging for regular geometries were compared with the well-established numerical models, which are based on the finite element method. Comparison among the analytical solutions obtained using zero boundary conditions and extrapolated boundary conditions (EBCs) was also performed. The results reveal that the analytical solutions are in close agreement with the numerical solutions, and solutions obtained using EBCs are more accurate in obtaining the mean time of flight data compared to their counterpart. The analytical solutions were also shown to be capable of providing bulk optical properties through a numerical experiment using a realistic breast model.

Efficient gradient-free simplex method for estimation of optical properties in image-guided diffuse optical tomography

Typical image-guided diffuse optical tomographic image reconstruction procedures involve reduction of the number of optical parameters to be reconstructed equal to the number of distinct regions identified in the structural information provided by the traditional imaging modality. This makes the image reconstruction problem less ill-posed compared to traditional underdetermined cases. Still, the methods that are deployed in this case are same as those used for traditional diffuse optical image reconstruction, which involves a regularization term as well as computation of the Jacobian. A gradient-free Nelder-Mead simplex method is proposed here to perform the image reconstruction procedure and is shown to provide solutions that closely match ones obtained using established methods, even in highly noisy data. The proposed method also has the distinct advantage of being more efficient owing to being regularization free, involving only repeated forward calculations.

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part I: zero and extrapolated boundary conditions

The mathematical model for diffuse fluorescence spectroscopy/imaging is represented by coupled partial differential equations (PDEs), which describe the excitation and emission light propagation in soft biological tissues. The generic closed-form solutions for these coupled PDEs are derived in this work for the case of regular geometries using the Green's function approach using both zero and extrapolated boundary conditions. The specific solutions along with the typical data types, such as integrated intensity and the mean time of flight, for various regular geometries were also derived for both time- and frequency-domain cases.

Data-resolution based optimal choice of minimum required measurements for image-guided diffuse optical tomography

Image-guided diffuse optical tomography has the advantage of reducing the total number of optical parameters being reconstructed to the number of distinct tissue types identified by the traditional imaging modality, converting the optical image-reconstruction problem from underdetermined in nature to overdetermined. In such cases, the minimum required measurements might be far less compared to those of the traditional diffuse optical imaging. An approach to choose these optimally based on a data-resolution matrix is proposed, and it is shown that such a choice does not compromise the reconstruction performance.

Prior image-constrained ℓ(1)-norm-based reconstruction method for effective usage of structural information in diffuse optical tomography

A novel approach that can more effectively use the structural information provided by the traditional imaging modalities in multimodal diffuse optical tomographic imaging is introduced. This approach is based on a prior image-constrained-ℓ(1) minimization scheme and has been motivated by the recent progress in the sparse image reconstruction techniques. It is shown that the proposed framework is more effective in terms of localizing the tumor region and recovering the optical property values both in numerical and gelatin phantom cases compared to the traditional methods that use structural information.

Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography

PURPOSE

To optimize the data-collection strategy for diffuse optical tomography and to obtain a set of independent measurements among the total measurements using the model based data-resolution matrix characteristics.

METHODS

The data-resolution matrix is computed based on the sensitivity matrix and the regularization scheme used in the reconstruction procedure by matching the predicted data with the actual one. The diagonal values of data-resolution matrix show the importance of a particular measurement and the magnitude of off-diagonal entries shows the dependence among measurements. Based on the closeness of diagonal value magnitude to off-diagonal entries, the independent measurements choice is made. The reconstruction results obtained using all measurements were compared to the ones obtained using only independent measurements in both numerical and experimental phantom cases. The traditional singular value analysis was also performed to compare the results obtained using the proposed method.

RESULTS

The results indicate that choosing only independent measurements based on data-resolution matrix characteristics for the image reconstruction does not compromise the reconstructed image quality significantly, in turn reduces the data-collection time associated with the procedure. When the same number of measurements (equivalent to independent ones) are chosen at random, the reconstruction results were having poor quality with major boundary artifacts. The number of independent measurements obtained using data-resolution matrix analysis is much higher compared to that obtained using the singular value analysis.

CONCLUSIONS

The data-resolution matrix analysis is able to provide the high level of optimization needed for effective data-collection in diffuse optical imaging. The analysis itself is independent of noise characteristics in the data, resulting in an universal framework to characterize and optimize a given data-collection strategy.

Minimal residual method provides optimal regularization parameter for diffuse optical tomography

The inverse problem in the diffuse optical tomography is known to be nonlinear, ill-posed, and sometimes under-determined, requiring regularization to obtain meaningful results, with Tikhonov-type regularization being the most popular one. The choice of this regularization parameter dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. An automated method for optimal selection of regularization parameter that is based on regularized minimal residual method (MRM) is proposed and is compared with the traditional generalized cross-validation method. The results obtained using numerical and gelatin phantom data indicate that the MRM-based method is capable of providing the optimal regularization parameter.

Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using ℓ(1)-norm-based linear image reconstruction method

Traditional image reconstruction methods in rapid dynamic diffuse optical tomography employ ℓ(2)-norm-based regularization, which is known to remove the high-frequency components in the reconstructed images and make them appear smooth. The contrast recovery in these type of methods is typically dependent on the iterative nature of method employed, where the nonlinear iterative technique is known to perform better in comparison to linear techniques (noniterative) with a caveat that nonlinear techniques are computationally complex. Assuming that there is a linear dependency of solution between successive frames resulted in a linear inverse problem. This new framework with the combination of ℓ(1)-norm-based regularization can provide better robustness to noise and provide better contrast recovery compared to conventional ℓ(2)-based techniques. Moreover, it is shown that the proposed ℓ(1)-based technique is computationally efficient compared to its counterpart (ℓ(2)-based one). The proposed framework requires a reasonably close estimate of the actual solution for the initial frame, and any suboptimal estimate leads to erroneous reconstruction results for the subsequent frames.

Model-resolution based regularization improves near infrared diffuse optical tomography

Diffuse optical tomographic imaging is known to be an ill-posed problem, and a penalty/regularization term is used in image reconstruction (inverse problem) to overcome this limitation. Two schemes that are prevalent are spatially varying (exponential) and constant (standard) regularizations/penalties. A scheme that is also spatially varying but uses the model information is introduced based on the model-resolution matrix. This scheme, along with exponential and standard regularization schemes, is evaluated objectively based on model-resolution and data-resolution matrices. This objective analysis showed that resolution characteristics are better for spatially varying penalties compared to standard regularization; and among spatially varying regularization schemes, the model-resolution based regularization fares well in providing improved data-resolution and model-resolution characteristics. The verification of the same is achieved by performing numerical experiments in reconstructing 1% noisy data involving simple two- and three-dimensional imaging domains.

Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units

Diffuse optical tomographic image reconstruction uses advanced numerical models that are computationally costly to be implemented in the real time. The graphics processing units (GPUs) offer desktop massive parallelization that can accelerate these computations. An open-source GPU-accelerated linear algebra library package is used to compute the most intensive matrix-matrix calculations and matrix decompositions that are used in solving the system of linear equations. These open-source functions were integrated into the existing frequency-domain diffuse optical image reconstruction algorithms to evaluate the acceleration capability of the GPUs (NVIDIA Tesla C 1060) with increasing reconstruction problem sizes. These studies indicate that single precision computations are sufficient for diffuse optical tomographic image reconstruction. The acceleration per iteration can be up to 40, using GPUs compared to traditional CPUs in case of three-dimensional reconstruction, where the reconstruction problem is more underdetermined, making the GPUs more attractive in the clinical settings. The current limitation of these GPUs in the available onboard memory (4 GB) that restricts the reconstruction of a large set of optical parameters, more than 13,377.

Assessment of ultrasound modulation of near infrared light on the quantification of scattering coefficient

PURPOSE

To assess the effect of ultrasound modulation of near infrared (NIR) light on the quantification of scattering coefficient in tissue-mimicking biological phantoms.

METHODS

A unique method to estimate the phase of the modulated NIR light making use of only time averaged intensity measurements using a charge coupled device camera is used in this investigation. These experimental measurements from tissue-mimicking biological phantoms are used to estimate the differential pathlength, in turn leading to estimation of optical scattering coefficient. A Monte-Carlo model based numerical estimation of phase in lieu of ultrasound modulation is performed to verify the experimental results.

RESULTS

The results indicate that the ultrasound modulation of NIR light enhances the effective scattering coefficient. The observed effective scattering coefficient enhancement in tissue-mimicking viscoelastic phantoms increases with increasing ultrasound drive voltage. The same trend is noticed as the ultrasound modulation frequency approaches the natural vibration frequency of the phantom material. The contrast enhancement is less for the stiffer (larger storage modulus) tissue, mimicking tumor necrotic core, compared to the normal tissue.

CONCLUSIONS

The ultrasound modulation of the insonified region leads to an increase in the effective number of scattering events experienced by NIR light, increasing the measured phase, causing the enhancement in the effective scattering coefficient. The ultrasound modulation of NIR light could provide better estimation of scattering coefficient. The observed local enhancement of the effective scattering coefficient, in the ultrasound focal region, is validated using both experimental measurements and Monte-Carlo simulations.

Singular value decomposition based computationally efficient algorithm for rapid dynamic near-infrared diffuse optical tomography

PURPOSE

A computationally efficient algorithm (linear iterative type) based on singular value decomposition (SVD) of the Jacobian has been developed that can be used in rapid dynamic near-infrared (NIR) diffuse optical tomography.

METHODS

Numerical and experimental studies have been conducted to prove the computational efficacy of this SVD-based algorithm over conventional optical image reconstruction algorithms.

RESULTS

These studies indicate that the performance of linear iterative algorithms in terms of contrast recovery (quantitation of optical images) is better compared to nonlinear iterative (conventional) algorithms, provided the initial guess is close to the actual solution. The nonlinear algorithms can provide better quality images compared to the linear iterative type algorithms. Moreover, the analytical and numerical equivalence of the SVD-based algorithm to linear iterative algorithms was also established as a part of this work. It is also demonstrated that the SVD-based image reconstruction typically requires O(NN2) operations per iteration, as contrasted with linear and nonlinear iterative methods that, respectively, require O(NN3) and O(NN6) operations, with "NN" being the number of unknown parameters in the optical image reconstruction procedure.

CONCLUSIONS

This SVD-based computationally efficient algorithm can make the integration of image reconstruction procedure with the data acquisition feasible, in turn making the rapid dynamic NIR tomography viable in the clinic to continuously monitor hemodynamic changes in the tissue pathophysiology.

Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction

Diffuse optical tomography, also known as near infrared tomography, has been under investigation, for non-invasive functional imaging of tissue, specifically for the detection and characterization of breast cancer or other soft tissue lesions. Much work has been carried out for accurate modeling and image reconstruction from clinical data. NIRFAST, a modeling and image reconstruction package has been developed, which is capable of single wavelength and multi-wavelength optical or functional imaging from measured data. The theory behind the modeling techniques as well as the image reconstruction algorithms is presented here, and 2D and 3D examples are presented to demonstrate its capabilities. The results show that 3D modeling can be combined with measured data from multiple wavelengths to reconstruct chromophore concentrations within the tissue. Additionally it is possible to recover scattering spectra, resulting from the dominant Mie-type scatter present in tissue. Overall, this paper gives a comprehensive over view of the modeling techniques used in diffuse optical tomographic imaging, in the context of NIRFAST software package.