Compressive sensing for biomedical imaging

MRI Simulation-based evaluation of an efficient under-sampling approach

Compressive sampling (CS) has been commonly employed in the field of magnetic resonance imaging (MRI) to accurately reconstruct sparse and compressive signals. In a MR image, a large amount of encoded information focuses on the origin of the k-space. For the 2D Cartesian K-space MRI, under-sampling the frequency-encoding (k_x) dimension does not affect to the acquisition time, thus, only the phase-encoding (k_y) dimension can be exploited. In the traditional random under-sampling approach, it acquired Gaussian random measurements along the phaseencoding (k_y) in the k-space. In this paper, we proposed a hybrid under-sampling approach; the number of measurements in (k_y) is divided into two portions: 70% of the measurements are for random under-sampling and 30% are for definite under-sampling near the origin of the k-space. The numerical simulation consequences pointed out that, in the lower region of the under-sampling ratio r, both the average error and the universal image quality index of the appointed scheme are drastically improved up to 55 and 77% respectively as compared to the traditional scheme. For the first time, instead of using highly computational complexity of many advanced reconstruction techniques, a simple and efficient CS method based simulation is proposed for MRI reconstruction improvement. These findings are very useful for designing new MRI data acquisition approaches for reducing the imaging time of current MRI systems.

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

Accelerating cardiac diffusion tensor imaging combining local low-rank and 3D TV constraint

OBJECTIVE

Diffusion tensor magnetic resonance imaging (DT-MRI, or DTI) is a promising technique for invasively probing biological tissue structures. However, DTI is known to suffer from much longer acquisition time with respect to conventional MRI and the problem is worsened when dealing with in vivo acquisitions. Therefore, faster DTI for both ex vivo and in vivo scans is highly desired.

MATERIALS AND METHODS

This paper proposes a new compressed sensing (CS) reconstruction method that employs local low-rank (LLR) model and three-dimensional (3D) total variation (TV) constraint to reconstruct cardiac diffusion-weighted (DW) images from highly undersampled k-space data. The LLR model takes the set of DW images corresponding to different diffusion gradient directions as a 3D image volume and decomposes the latter into overlapping 3D blocks. Then, the 3D blocks are stacked as two-dimensional (2D) matrix. Finally, low-rank property is applied to each block matrix and the 3D TV constraint to the 3D image volume. The underlying constrained optimization problem is finally solved using the first-order fast method. The proposed method is evaluated on real ex vivo cardiac DTI data as a prerequisite to in vivo cardiac DTI applications.

RESULTS

The results on real human ex vivo cardiac DTI images demonstrate that the proposed method exhibits lower reconstruction errors for DTI indices, including fractional anisotropy (FA), mean diffusivities (MD), transverse angle (TA), and helix angle (HA), compared to existing CS-based DTI image reconstruction techniques.

CONCLUSION

The proposed method provides better reconstruction quality and more accurate DTI indices in comparison with the state-of-the-art CS-based DW image reconstruction methods.

Automatic computer aided analysis algorithms and system for adrenal tumors on CT images

BACKGROUND

The adrenal tumor will disturb the secreting function of adrenocortical cells, leading to many diseases. Different kinds of adrenal tumors require different therapeutic schedules.

OBJECTIVE

In the practical diagnosis, it highly relies on the doctor's experience to judge the tumor type by reading the hundreds of CT images.

METHODS

This paper proposed an automatic computer aided analysis method for adrenal tumors detection and classification. It consisted of the automatic segmentation algorithms, the feature extraction and the classification algorithms. These algorithms were then integrated into a system and conducted on the graphic interface by using MATLAB Graphic user interface (GUI).

RESULTS

The accuracy of the automatic computer aided segmentation and classification reached 90% on 436 CT images.

CONCLUSION

The experiments proved the stability and reliability of this automatic computer aided analytic system.

Sparse dictionary for synthetic transmit aperture medical ultrasound imaging

It is possible to recover a signal below the Nyquist sampling limit using a compressive sensing technique in ultrasound imaging. However, the reconstruction enabled by common sparse transform approaches does not achieve satisfactory results. Considering the ultrasound echo signal's features of attenuation, repetition, and superposition, a sparse dictionary with the emission pulse signal is proposed. Sparse coefficients in the proposed dictionary have high sparsity. Images reconstructed with this dictionary were compared with those obtained with the three other common transforms, namely, discrete Fourier transform, discrete cosine transform, and discrete wavelet transform. The performance of the proposed dictionary was analyzed via a simulation and experimental data. The mean absolute error (MAE) was used to quantify the quality of the reconstructions. Experimental results indicate that the MAE associated with the proposed dictionary was always the smallest, the reconstruction time required was the shortest, and the lateral resolution and contrast of the reconstructed images were also the closest to the original images. The proposed sparse dictionary performed better than the other three sparse transforms. With the same sampling rate, the proposed dictionary achieved excellent reconstruction quality.

Analysis of generalized rosette trajectory for compressed sensing MRI

PURPOSE

The application of compressed sensing (CS) technology in magnetic resonance imaging (MRI) is to accelerate the MRI scan speed by incoherent undersampling of k-space data and nonlinear iterative reconstruction of MRI images. This paper generalizes the existing rosette trajectories to configure the sampling patterns for undersampled k-space data acquisition in MRI scans. The arch and curvature characteristics of the generalized rosette trajectories are analyzed to explore their feasibility and advantages for CS reconstruction of MRI images.

METHODS

Two key properties crucial to the CS MRI application, the scan speed and sampling incoherence of the generalized rosette trajectories, are analyzed. The analysis on the scan speed of generalized rosette trajectories is based on the transversal time derived from the curvature of the trajectories, and the sampling incoherence is based on the evaluation of the point spread function for the measurement matrix. The results of analysis are supported by extensive simulations where the performances of rosette, spiral, and radial sampling patterns at different acceleration factors are compared.

RESULTS

It is shown that compared with spiral trajectories, the arch and curvature characteristics of the generalized rosette trajectories are more feasible to meet the physical requirements of undersampled k-space data acquisition in terms of time shortness and scan area. It is further shown that the sampling pattern of the rosette trajectory has higher incoherence than that of the other trajectories and can thus achieve higher reconstruction performance. Reconstruction performances illustrate that the rosette trajectory can achieve about 10% higher peak signal-to-noise ratio than radial and spiral trajectories under the high acceleration factor R = 10.

CONCLUSIONS

The generalized rosette trajectories can be a desirable candidate for CS reconstruction of MRI.

A Model of Regularization Parameter Determination in Low-Dose X-Ray CT Reconstruction Based on Dictionary Learning

In recent years, X-ray computed tomography (CT) is becoming widely used to reveal patient's anatomical information. However, the side effect of radiation, relating to genetic or cancerous diseases, has caused great public concern. The problem is how to minimize radiation dose significantly while maintaining image quality. As a practical application of compressed sensing theory, one category of methods takes total variation (TV) minimization as the sparse constraint, which makes it possible and effective to get a reconstruction image of high quality in the undersampling situation. On the other hand, a preliminary attempt of low-dose CT reconstruction based on dictionary learning seems to be another effective choice. But some critical parameters, such as the regularization parameter, cannot be determined by detecting datasets. In this paper, we propose a reweighted objective function that contributes to a numerical calculation model of the regularization parameter. A number of experiments demonstrate that this strategy performs well with better reconstruction images and saving of a large amount of time.

Variable density incoherent spatiotemporal acquisition (VISTA) for highly accelerated cardiac MRI

PURPOSE

For the application of compressive sensing to parallel MRI, Poisson disk sampling (PDS) has been shown to generate superior results compared with random sampling methods. However, due to its limited flexibility to incorporate additional constraints, PDS is not readily extendible to dynamic applications. Here, we propose and validate a pseudo-random sampling technique that allows incorporating constraints specific to dynamic imaging.

METHODS

The proposed sampling scheme, called variable density incoherent spatiotemporal acquisition (VISTA), is based on constrained minimization of Riesz energy on a spatiotemporal grid. Data from both a digital phantom and real-time cine were used to compare VISTA with uniform interleaved sampling (UIS) and variable density random sampling (VRS). The image quality was assessed qualitatively and quantitatively.

RESULTS

VISTA improved the trade-off between noise and sharpness. Also, VISTA produced diagnostic quality images at an acceleration rate of 15, whereas UIS and VRS images degraded below the diagnostic threshold at lower acceleration rates.

CONCLUSIONS

VISTA generates spatiotemporal sampling patterns with high levels of uniformity and incoherence, while maintaining a constant temporal resolution. Using a small pilot study, VISTA was shown to produce diagnostic quality images at acceleration rates up to 15.

Dictionary-learning-based reconstruction method for electron tomography

Electron tomography usually suffers from so-called “missing wedge” artifacts caused by limited tilt angle range. An equally sloped tomography (EST) acquisition scheme (which should be called the linogram sampling scheme) was recently applied to achieve 2.4-angstrom resolution. On the other hand, a compressive sensing inspired reconstruction algorithm, known as adaptive dictionary based statistical iterative reconstruction (ADSIR), has been reported for X-ray computed tomography. In this paper, we evaluate the EST, ADSIR, and an ordered-subset simultaneous algebraic reconstruction technique (OS-SART), and compare the ES and equally angled (EA) data acquisition modes. Our results show that OS-SART is comparable to EST, and the ADSIR outperforms EST and OS-SART. Furthermore, the equally sloped projection data acquisition mode has no advantage over the conventional equally angled mode in this context.

Sparse-view ultrasound diffraction tomography using compressed sensing with nonuniform FFT

Accurate reconstruction of the object from sparse-view sampling data is an appealing issue for ultrasound diffraction tomography (UDT). In this paper, we present a reconstruction method based on compressed sensing framework for sparse-view UDT. Due to the piecewise uniform characteristics of anatomy structures, the total variation is introduced into the cost function to find a more faithful sparse representation of the object. The inverse problem of UDT is iteratively resolved by conjugate gradient with nonuniform fast Fourier transform. Simulation results show the effectiveness of the proposed method that the main characteristics of the object can be properly presented with only 16 views. Compared to interpolation and multiband method, the proposed method can provide higher resolution and lower artifacts with the same view number. The robustness to noise and the computation complexity are also discussed.

The meaning of interior tomography

The classic imaging geometry for computed tomography is for the collection of un-truncated projections and the reconstruction of a global image, with the Fourier transform as the theoretical foundation that is intrinsically non-local. Recently, interior tomography research has led to theoretically exact relationships between localities in the projection and image spaces and practically promising reconstruction algorithms. Initially, interior tomography was developed for x-ray computed tomography. Then, it was elevated to have the status of a general imaging principle. Finally, a novel framework known as 'omni-tomography' is being developed for a grand fusion of multiple imaging modalities, allowing tomographic synchrony of diversified features.

Scout-view assisted interior micro-CT

Micro computed tomography (micro-CT) is a widely-used imaging technique. A challenge of micro-CT is to quantitatively reconstruct a sample larger than the field-of-view (FOV) of the detector. This scenario is characterized by truncated projections and associated image artifacts. However, for such truncated scans, a low resolution scout scan with an increased FOV is frequently acquired so as to position the sample properly. This study shows that the otherwise discarded scout scans can provide sufficient additional information to uniquely and stably reconstruct the interior region of interest. Two interior reconstruction methods are designed to utilize the multi-resolution data without significant computational overhead. While most previous studies used numerically truncated global projections as interior data, this study uses truly hybrid scans where global and interior scans were carried out at different resolutions. Additionally, owing to the lack of standard interior micro-CT phantoms, we designed and fabricated novel interior micro-CT phantoms for this study to provide means of validation for our algorithms. Finally, two characteristic samples from separate studies were scanned to show the effect of our reconstructions. The presented methods show significant improvements over existing reconstruction algorithms.

Compressive sensing image sensors-hardware implementation

The compressive sensing (CS) paradigm uses simultaneous sensing and compression to provide an efficient image acquisition technique. The main advantages of the CS method include high resolution imaging using low resolution sensor arrays and faster image acquisition. Since the imaging philosophy in CS imagers is different from conventional imaging systems, new physical structures have been developed for cameras that use the CS technique. In this paper, a review of different hardware implementations of CS encoding in optical and electrical domains is presented. Considering the recent advances in CMOS (complementary metal–oxide–semiconductor) technologies and the feasibility of performing on-chip signal processing, important practical issues in the implementation of CS in CMOS sensors are emphasized. In addition, the CS coding for video capture is discussed.

Group-sparse representation with dictionary learning for medical image denoising and fusion

Recently, sparse representation has attracted a lot of interest in various areas. However, the standard sparse representation does not consider the intrinsic structure, i.e., the nonzero elements occur in clusters, called group sparsity. Furthermore, there is no dictionary learning method for group sparse representation considering the geometrical structure of space spanned by atoms. In this paper, we propose a novel dictionary learning method, called Dictionary Learning with Group Sparsity and Graph Regularization (DL-GSGR). First, the geometrical structure of atoms is modeled as the graph regularization. Then, combining group sparsity and graph regularization, the DL-GSGR is presented, which is solved by alternating the group sparse coding and dictionary updating. In this way, the group coherence of learned dictionary can be enforced small enough such that any signal can be group sparse coded effectively. Finally, group sparse representation with DL-GSGR is applied to 3-D medical image denoising and image fusion. Specifically, in 3-D medical image denoising, a 3-D processing mechanism (using the similarity among nearby slices) and temporal regularization (to perverse the correlations across nearby slices) are exploited. The experimental results on 3-D image denoising and image fusion demonstrate the superiority of our proposed denoising and fusion approaches.

A comprehensive study on the relationship between the image quality and imaging dose in low-dose cone beam CT

While compressed sensing (CS)-based algorithms have been developed for the low-dose cone beam CT (CBCT) reconstruction, a clear understanding of the relationship between the image quality and imaging dose at low-dose levels is needed. In this paper, we qualitatively investigate this subject in a comprehensive manner with extensive experimental and simulation studies. The basic idea is to plot both the image quality and imaging dose together as functions of the number of projections and mAs per projection over the whole clinically relevant range. On this basis, a clear understanding of the tradeoff between the image quality and imaging dose can be achieved and optimal low-dose CBCT scan protocols can be developed to maximize the dose reduction while minimizing the image quality loss for various imaging tasks in image-guided radiation therapy (IGRT). Main findings of this work include (1) under the CS-based reconstruction framework, image quality has little degradation over a large range of dose variation. Image quality degradation becomes evident when the imaging dose (approximated with the x-ray tube load) is decreased below 100 total mAs. An imaging dose lower than 40 total mAs leads to a dramatic image degradation, and thus should be used cautiously. Optimal low-dose CBCT scan protocols likely fall in the dose range of 40-100 total mAs, depending on the specific IGRT applications. (2) Among different scan protocols at a constant low-dose level, the super sparse-view reconstruction with the projection number less than 50 is the most challenging case, even with strong regularization. Better image quality can be acquired with low mAs protocols. (3) The optimal scan protocol is the combination of a medium number of projections and a medium level of mAs/view. This is more evident when the dose is around 72.8 total mAs or below and when the ROI is a low-contrast or high-resolution object. Based on our results, the optimal number of projections is around 90 to 120. (4) The clinically acceptable lowest imaging dose level is task dependent. In our study, 72.8 mAs is a safe dose level for visualizing low-contrast objects, while 12.2 total mAs is sufficient for detecting high-contrast objects of diameter greater than 3 mm.