Blind deblurring of spiral CT images

Harmonization of in-plane resolution in CT using multiple reconstructions from single acquisitions

PURPOSE

To providea methodology that removes the spatial variability of in-plane resolution using different CT reconstructions. The methodology does not require any training, sinogram, or specific reconstruction method.

METHODS

The methodology is formulated as a reconstruction problem. The desired sharp image is modeled as an unobservable variable to be estimated from an arbitrary number of observations with spatially variant resolution. The methodology comprises three steps: (1) density harmonization, which removes the density variability across reconstructions; (2) point spread function (PSF) estimation, which estimates a spatially variant PSF with arbitrary shape; (3) deconvolution, which is formulated as a regularized least squares problem. The assessment was performed with CT scans of phantoms acquired with three different Siemens scanners (Definition AS, Definition AS+, Drive). Four low-dose acquisitions reconstructed with backprojection and iterative methods were used for the resolution harmonization. A sharp, high-dose (HD) reconstruction was used as a validation reference. The different factors affecting the in-plane resolution (radial, angular, and longitudinal) were studied with regression analysis of the edge decay (between 10% and 90% of the edge spread function (ESF) amplitude).

RESULTS

Results showed that the in-plane resolution improves remarkably and the spatial variability is substantially reduced without compromising the noise characteristics. The modulated transfer function (MTF) also confirmed a pronounced increase in resolution. The resolution improvement was also tested by measuring the wall thickness of tubes simulating airways. In all scanners, the resolution harmonization obtained better performance than the HD, sharp reconstruction used as a reference (up to 50 percentage points). The methodology was also evaluated in clinical scans achieving a noise reduction and a clear improvement in thin-layered structures. The estimated ESF and MTF confirmed the resolution improvement.

CONCLUSION

We propose a versatile methodology to reduce the spatial variability of in-plane resolution in CT scans by leveraging different reconstructions available in clinical studies. The methodology does not require any sinogram, training, or specific reconstruction, and it is not limited to a fixed number of input images. Therefore, it can be easily adopted in multicenter studies and clinical practice. The results obtained with our resolution harmonization methodology evidence its suitability to reduce the spatially variant in-plane resolution in clinical CT scans without compromising the reconstruction's noise characteristics. We believe that the resolution increase achieved by our methodology may contribute in more accurate and reliable measurements of small structures such as vasculature, airways, and wall thickness.

CT Super-Resolution GAN Constrained by the Identical, Residual, and Cycle Learning Ensemble (GAN-CIRCLE)

In this paper, we present a semi-supervised deep learning approach to accurately recover high-resolution (HR) CT images from low-resolution (LR) counterparts. Specifically, with the generative adversarial network (GAN) as the building block, we enforce the cycle-consistency in terms of the Wasserstein distance to establish a nonlinear end-to-end mapping from noisy LR input images to denoised and deblurred HR outputs. We also include the joint constraints in the loss function to facilitate structural preservation. In this process, we incorporate deep convolutional neural network (CNN), residual learning, and network in network techniques for feature extraction and restoration. In contrast to the current trend of increasing network depth and complexity to boost the imaging performance, we apply a parallel 1×1 CNN to compress the output of the hidden layer and optimize the number of layers and the number of filters for each convolutional layer. The quantitative and qualitative evaluative results demonstrate that our proposed model is accurate, efficient and robust for super-resolution (SR) image restoration from noisy LR input images. In particular, we validate our composite SR networks on three large-scale CT datasets, and obtain promising results as compared to the other state-of-the-art methods.

A Novel Blind Restoration and Reconstruction Approach for CT Images Based on Sparse Representation and Hierarchical Bayesian-MAP

Computed tomography (CT) image reconstruction and restoration are very important in medical image processing, and are associated together to be an inverse problem. Image iterative reconstruction is a key tool to increase the applicability of CT imaging and reduce radiation dose. Nevertheless, traditional image iterative reconstruction methods are limited by the sampling theorem and also the blurring of projection data will propagate unhampered artifact in the reconstructed image. To overcome these problems, image restoration techniques should be developed to accurately correct a wide variety of image degrading effects in order to effectively improve image reconstruction. In this paper, a blind image restoration technique is embedded in the compressive sensing CT image reconstruction, which can result in a high-quality reconstruction image using fewer projection data. Because a small amount of data can be obtained by radiation in a shorter time, high-quality image reconstruction with less data is equivalent to reducing radiation dose. Technically, both the blurring process and the sparse representation of the sharp CT image are first modeled as a serial of parameters. The sharp CT image will be obtained from the estimated sparse representation. Then, the model parameters are estimated by a hierarchical Bayesian maximum posteriori formulation. Finally, the estimated model parameters are optimized to obtain the final image reconstruction. We demonstrate the effectiveness of the proposed method with the simulation experiments in terms of the peak signal to noise ratio (PSNR), and structural similarity index (SSIM).

4D-CT-based motion correction of PET images using 3D iterative deconvolution

Objectives

Positron emission tomography acquisition takes several minutes representing an image averaged over multiple breathing cycles. Therefore, in areas influenced by respiratory movement, PET-positive lesions occur larger, but less intensive than they actually are, resulting in false quantitative assessment. We developed a motion-correction algorithm based on 4D-CT without the need to adapt PET-acquisition.

Methods

The algorithm is based on a full 3D iterative Richardson-Lucy-Deconvolution using a point-spread-function constructed using the motion information obtained from the 4D-CT. In a motion phantom study (3 different hot spheres in background activity), optimal parameters for the algorithm in terms of number of iterations and start image were estimated. Finally, the correction method was applied to 3 patient data sets. In phantom and patient data sets lesions were delineated and compared between motion corrected and uncorrected images for activity uptake and volume.

Results

Phantom studies showed best results for motion correction after 6 deconvolution steps or higher. In phantom studies, lesion volume improved up to 23% for the largest, 43% for the medium and 49% for the smallest sphere due to the correction algorithm. In patient data the correction resulted in a significant reduction of the tumor volume up to 33.3 % and an increase of the maximum and mean uptake of the lesion up to 62.1 and 19.8 % respectively.

Conclusion

In conclusion, the proposed motion correction method showed good results in phantom data and a promising reduction of detected lesion volume and a consequently increasing activity uptake in three patients with lung lesions.

Cochlear implant phantom for evaluating computed tomography acquisition parameters

Cochlear implants (CIs) are surgically implantable neuroprosthetic devices used to treat profound hearing loss. Recent literature indicates that there is a correlation between the final intracochlear positioning of the CI electrode arrays and the ultimate hearing outcome of the patient, indicating that further studies to better understand the relationship between electrode position and outcomes could have significant implications for future surgical techniques, array design, and processor programming methods. Postimplantation high-resolution computed tomography (CT) imaging is the best modality for localizing electrodes and provides the resolution necessary to visually identify electrode position, although with an unknown degree of accuracy depending on image acquisition parameters, like the hounsfield unit (HU) range of reconstruction, orientation, radiation dose, and image resolution. We report on the development of a phantom and on its use to study how four acquisition parameters, including image resolution and HU range of reconstruction, affect how accurately the true position of the electrodes can be found in a dataset of CT scans acquired from multiple helical and cone beam scanners. We also show how the phantom can be used to evaluate the effect of acquisition parameters on automatic electrode localization techniques.

Imaging model for the scintillator and its application to digital radiography image enhancement

Digital Radiography (DR) images obtained by OCD-based (optical coupling detector) Micro-CT system usually suffer from low contrast. In this paper, a mathematical model is proposed to describe the image formation process in scintillator. By solving the correlative inverse problem, the quality of DR images is improved, i.e. higher contrast and spatial resolution. By analyzing the radiative transfer process of visible light in scintillator, scattering is recognized as the main factor leading to low contrast. Moreover, involved blurring effect is also concerned and described as point spread function (PSF). Based on these physical processes, the scintillator imaging model is then established. When solving the inverse problem, pre-correction to the intensity of x-rays, dark channel prior based haze removing technique, and an effective blind deblurring approach are employed. Experiments on a variety of DR images show that the proposed approach could improve the contrast of DR images dramatically as well as eliminate the blurring vision effectively. Compared with traditional contrast enhancement methods, such as CLAHE, our method could preserve the relative absorption values well.

A New Study of Blind Deconvolution with Implicit Incorporation of Nonnegativity Constraints

The inverse problem of image restoration to remove noise and blur in an observed image was extensively studied in the last two decades. For the case of a known blurring kernel (or a known blurring type such as out of focus or Gaussian blur), many effective models and efficient solvers exist. However when the underlying blur is unknown, there have been fewer developments for modelling the so-called blind deblurring since the early works of You and Kaveh (1996) and Chan and Wong (1998). A major challenge is how to impose the extra constraints to ensure quality of restoration. This paper proposes a new transform based method to impose the positivity constraints automatically and then two numerical solution algorithms. Test results demonstrate the effectiveness and robustness of the proposed method in restoring blurred images.

A spatial mixture approach to inferring sub-ROI spatio-temporal patterns from rapid event-related fMRI data

Previous works investigated a range of spatio-temporal models for fMRI data analysis to provide robust determination of functional region-of-interest (ROI). We present a novel spatio-temporal fMRI model that is suitable for identifying a number of distinct temporal patterns and their spatial support in the voxel space. Accordingly, fMRI signals on a single voxel are modeled as a probabilistic superposition of those temporal patterns. The spatially varying influence of individual patterns is defined in terms of a parameterised function. The temporal pattern is characterised by both the underlying hemodynamic response function (HRF) and a time series of the individual stimulus-response magnitudes, which makes the proposed model particularly suitable for modeling rapid event-related fMRI data. Moreover, a parametric approach is adopted to represent the HRFs. The resulting methodology is conceptually principled and computationally efficient. We first verify the proposed model in a controlled experimental setting using synthetic data. The model is further applied to analyzing real fMRI data, with focus on functional homogeneity within individual ROIs.

A dictionary learning approach for Poisson image deblurring

The restoration of images corrupted by blur and Poisson noise is a key issue in medical and biological image processing. While most existing methods are based on variational models, generally derived from a maximum a posteriori (MAP) formulation, recently sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, we propose in this paper a model containing three terms: a patch-based sparse representation prior over a learned dictionary, the pixel-based total variation regularization term and a data-fidelity term capturing the statistics of Poisson noise. The resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting. Extensive experimental results suggest that in terms of visual quality, peak signal-to-noise ratio value and the method noise, the proposed algorithm outperforms state-of-the-art methods.

Tomographic reconstruction of three-dimensional volumes using the distorted born iterative method

Although real imaging problems involve objects that have variations in three dimensions, a majority of work examining inverse scattering methods for ultrasonic tomography considers 2-D imaging problems. Therefore, the study of 3-D inverse scattering methods is necessary for future applications of ultrasonic tomography. In this work, 3-D reconstructions using different arrays of rectangular elements focused on elevation were studied when reconstructing spherical imaging targets by producing a series of 2-D image slices using the 2-D distorted Born iterative method (DBIM). The effects of focal number f/#, speed of sound contrast c, and scatterer size were considered. For comparison, the 3-D wave equation was also inverted using point-like transducers to produce fully 3-D DBIM image reconstructions. In 2-D slicing, blurring in the vertical direction was highly correlated with the transmit/receive elevation point-spread function of the transducers for low c. The eventual appearance of overshoot artifacts in the vertical direction were observed with increasing c. These diffraction-related artifacts were less severe for smaller focal number values and larger spherical target sizes. When using 3-D DBIM, the overshoot artifacts were not observed and spatial resolution was improved. However, results indicate that array configuration in 3-D reconstructions is important for good image reconstruction. Practical arrays were designed and assessed for image reconstruction using 3-D DBIM.

Parametric blind deconvolution for confocal laser scanning microscopy

In this paper, we propose a method for the iterative restoration of fluorescence Confocal Laser Scanning Microscopic (CLSM) images and parametric estimation of the acquisition system's Point Spread Function (PSF). The CLSM is an optical fluorescence microscope that scans a specimen in 3D and uses a pinhole to reject most of the out-of-focus light. However, the quality of the images suffers from two basic physical limitations. The diffraction-limited nature of the optical system, and the reduced amount of light detected by the photomultiplier cause blur and photon counting noise respectively. These images can hence benefit from post-processing restoration methods based on deconvolution. An efficient method for parametric blind image deconvolution involves the simultaneous estimation of the specimen 3D distribution of fluorescent sources and the microscope PSF. By using a model for the microscope image acquisition physical process, we reduce the number of free parameters describing the PSF and introduce constraints. The parameters of the PSF may vary during the course of experimentation, and so they have to be estimated directly from the observed data. A priori model of the specimen is further applied to stabilize the alternate minimization algorithm and to converge to the solutions.

Blind Deconvolution for Symmetric Point-spread Functions

Blind deconvolution is to restore a blurred image without full information of the associated point-spread function (PSF). One recent method is to formulate an equation with only the image as unknowns by eliminating the PSF because of its symmetric property. The original image is then recovered by solving the latter equation. We present a theoretical analysis for this method in this paper. After formulating the problem in terms of the Z-transforms, it is proved that the deconvolved solutions with this method are up to a constant under additional practical assumptions on the images. We also provide a preliminary numerical experiment with a practical phantom to demonstrate the feasibility of this method.

A New Method for Deblurring and Denoising of Medical Images using Complex Wavelet Transform

Deblurring in the presence of non-Gaussian noise is a hard problem, specially in ultrasonic and CT images. In this paper, a new method of image restoration, using complex wavelet transform, has been devised and applied to deblur in the presence of high speckle noise. It has been shown that the new method outperforms the Weiner filtering and Fourier-wavelet regularized deconvolution (ForWaRD) methods for both ultrasonic and CT images. Unlike Fourier and real wavelet transforms, complex wavelet transform is nearly shift-invariant. This gives complex wavelet transform an edge over other traditional methods when applied simultaneously for deblurring as well as denoising. The proposed method is independent of any assumption about the degradation process. It is adaptive, as it uses shrinkage function based on median and mean of absolute wavelet coefficient as well as standard deviation of wavelet coefficients. Its application on real spiral CT images of inner ear has shown a clear improvement over other methods.

Deblurring of breathing motion artifacts in thoracic PET images by deconvolution methods

In FDG-PET imaging of thoracic tumors, blurring due to breathing motion often significantly degrades the quality of the observed image, which then obscures the tumor boundary. We demonstrate a deblurring technique that combines patient-specific motion estimates of tissue trajectories with image deconvolution techniques, thereby partially eliminating breathing-motion induced artifacts. Two data sets were used to evaluate the methodology including mobile phantoms and clinical images. The clinical images consist of PET/CT co-registered images of patients diagnosed with lung cancer. A breathing motion model was used to locally estimate the location-dependent tissue location probability function (TLP) due to breathing. The deconvolution process is carried by an expectation-maximization (EM) iterative algorithm using the motion-based TLP. Several methods were used to improve the robustness of the deblurring process by mitigating noise amplification and compensating for motion estimate uncertainties. The mobile phantom study with controlled settings demonstrated significant reduction in underestimation error of concentration in high activity case without significant superiority between the different applied methods. In case of medium activity concentration (moderate noise levels), less improvement was reported (10%-15% reduction in underestimation error relative to 15%-20% reduction in high concentration). Residual denoising using wavelets offered the best performance for this case. In the clinical data case, the image spatial resolution was significantly improved, especially in the direction of greatest motion (cranio-caudal). The EM algorithm converged within 15 and 5 iterations in the large and small tumor cases, respectively. A compromise between a figure-of-merit and entropy minimization was suggested as a stopping criterion. Regularization techniques such as wavelets and Bayesian methods provided further refinement by suppressing noise amplification. Our initial results show that the proposed method provides a feasible framework for improving PET thoracic images, without the need for gated/4-D PET imaging, when 4-D CT is available to estimate tumor motion.

Evolution-operator-based single-step method for image processing

This work proposes an evolution-operator-based single-time-step method for image and signal processing. The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accuracy, free of instability constraint. From the point of image/signal processing, the LSEK gives rise to a family of lowpass filters. These filters contain controllable time delay and amplitude scaling. The new evolution operator-based method is constructed by pointwise adaptation of anisotropy to the coefficients of the LSEK. The Perona-Malik-type of anisotropic diffusion schemes is incorporated in the LSEK for image denoising. A forward-backward diffusion process is adopted to the LSEK for image deblurring or sharpening. A coupled PDE system is modified for image edge detection. The resulting image edge is utilized for image enhancement. Extensive computer experiments are carried out to demonstrate the performance of the proposed method. The major advantages of the proposed method are its single-step solution and readiness for multidimensional data analysis.

Iterative reconstruction method for light emitting sources based on the diffusion equation

Bioluminescent imaging (BLI) of luciferase-expressing cells in live small animals is a powerful technique for investigating tumor growth, metastasis, and specific biological molecular events. Three-dimensional imaging would greatly enhance applications in biomedicine since light emitting cell populations could be unambiguously associated with specific organs or tissues. Any imaging approach must account for the main optical properties of biological tissue because light emission from a distribution of sources at depth is strongly attenuated due to optical absorption and scattering in tissue. Our image reconstruction method for interior sources is based on the deblurring expectation maximization method and takes into account both of these effects. To determine the boundary of the object we use the standard iterative algorithm-maximum likelihood reconstruction method with an external source of diffuse light. Depth-dependent corrections were included in the reconstruction procedure to obtain a quantitative measure of light intensity by using the diffusion equation for light transport in semi-infinite turbid media with extrapolated boundary conditions.

The point spread function of spiral CT

Computed tomography (CT) scanners are usually described by their in-plane resolution and slice-sensitivity profile (SSP). Other imaging systems are characterized by their point spread function (PSF). The PSF is an excellent basis for the analysis, design and enhancement of imaging systems. The 3D PSF of CT systems has rarely been considered, and has usually been approximated by a 3D Gaussian. We present mathematical analysis of the PSF of single-slice and multi-slice fan-beam and cone-beam CT, for major reconstruction algorithms. We show that the PSF has a complicated, non-separable 3D shape. It is anisotropic in the xy plane and twisted in the z direction. Furthermore, the PSF is space variant in all three axes. In particular, it rotates as the input impulse function moves in the z direction. The PSF may also have effective discontinuities that can lead to streaking artefacts. Indirect measurements of the PSF can be misleading. We support the theoretical results by direct experimental measurements of the PSF.