Accelerated barrier optimization compressed sensing (ABOCS) reconstruction: Performance evaluation for cone-beam CT

Recent advances in compressed sensing (CS) enable accurate CT image reconstruction from highly undersampled and noisy projection measurements, due to the sparsifiable feature of most CT images using total variation (TV). These novel reconstruction methods have demonstrated advantages in clinical applications where radiation dose reduction is critical, such as onboard cone-beam CT (CBCT) imaging in radiation therapy. The image reconstruction using CS is formulated as either a constrained problem to minimize the TV objective within a small and fixed data fidelity error, or an unconstrained problem to minimize the data fidelity error with TV regularization. However, the conventional solutions to the above two formulations are either computationally inefficient or involved with inconsistent regularization parameter tuning, which significantly limit the clinical use of CS-based iterative reconstruction. In this paper, we propose an optimization algorithm for CS reconstruction which overcomes the above two drawbacks. The data fidelity tolerance of CS reconstruction can be well estimated based on the measured data, as most of the projection errors are from Poisson noise after effective data correction for scatter and beam-hardening effects. We therefore adopt the TV optimization framework with a data fidelity constraint. To accelerate the convergence, we first convert such a constrained optimization using a logarithmic barrier method into a form similar to that of the conventional TV regularization based reconstruction but with an automatically adjusted penalty weight. The problem is then solved efficiently by gradient projection with an adaptive Barzilai-Borwein step-size selection scheme. The proposed algorithm is referred to as accelerated barrier optimization for CS (ABOCS), and evaluated using both digital and physical phantom studies. ABOCS directly estimates the data fidelity tolerance from the raw projection data. Therefore, as demonstrated in both digital Shepp-Logan and physical head phantom studies, consistent reconstruction performances are achieved using the same algorithm parameters on scans with different noise levels and∕or on different objects. On the contrary, the penalty weight in a TV regularization based method needs to be fine-tuned in a large range (up to seven times) to maintain the reconstructed image quality. The improvement of ABOCS on computational efficiency is demonstrated in the comparisons with adaptive-steepest-descent-projection-onto-convex-sets (ASD-POCS), an existing CS reconstruction algorithm also using constrained optimization. ASD-POCS alternatively minimizes the TV objective using adaptive steepest descent (ASD) and the data fidelity error using projection onto convex sets (POCS). For similar image qualities of the Shepp-Logan phantom, ABOCS requires less computation time than ASD-POCS in MATLAB by more than one order of magnitude. We propose ABOCS for CBCT reconstruction. As compared to other published CS-based algorithms, our method has attractive features of fast convergence and consistent parameter settings for different datasets. These advantages have been demonstrated on phantom studies.

Recently, there are a lot of study of direction of arrival (DoA) estimation using compressive sensing (CS). As CS is a new paradigm in signal processing, there are many aspects of this method that can be investigated. In the case of DoA estimation in noisy measurement, it is important to correctly determine a correct threshold of CS reconstruction, particularly when CS reconstruction is implemented using L 1 -norm minimization. Too small threshold value will make the correct DoA does not lies in CS reconstruction searching area, while too large threshold value will burden CS iteration to select a solution from a large number of possible solutions. In this paper, we derived an optimal threshold value for CS reconstruction for DoA estimation mathematically and verified the result using computer simulation. Using Gaussian noise model, we obtain the chi-square distribution of euclidean distance of noisy and noiseless received vector. We introduce the thresholding index κ to scale the standard deviation of chi-square distribution to determine the CS reconstruction threshold and simulate this value for various SNR. We find that the optimal κ value 0.5 to 1 for high noise environment, and optimal κ value 1 to 2 in low noise environment.

In this paper, we address the problem of green Compressed Sensing (CS) reconstruction within Internet of Things (IoT) networks, both in terms of computing architecture and reconstruction algorithms. The approach is novel since, unlike most of the literature dealing with energy efficient gathering of the CS measurements, we focus on the energy efficiency of the signal reconstruction stage given the CS measurements. As a first novel contribution, we present an analysis of the energy consumption within the IoT network under two computing architectures. In the first one, reconstruction takes place within the IoT network and the reconstructed data are encoded and transmitted out of the IoT network; in the second one, all the CS measurements are forwarded to off-network devices for reconstruction and storage, i.e., reconstruction is off-loaded. Our analysis shows that the two architectures significantly differ in terms of consumed energy, and it outlines a theoretically motivated criterion to select a green CS reconstruction computing architecture. Specifically, we present a suitable decision function to determine which architecture outperforms the other in terms of energy efficiency. The presented decision function depends on a few IoT network features, such as the network size, the sink connectivity, and other systems’ parameters. As a second novel contribution, we show how to overcome classical performance comparison of different CS reconstruction algorithms usually carried out w.r.t. the achieved accuracy. Specifically, we consider the consumed energy and analyze the energy vs. accuracy trade-off. The herein presented approach, jointly considering signal processing and IoT network issues, is a relevant contribution for designing green compressive sampling architectures in IoT networks.

Coronary vessel wall magnetic resonance (MR) imaging is important for heart disease diagnosis but often suffers long scan time. Compressed sensing (CS) has been previously used to accelerate MR imaging by reconstructing an MR image from undersampled k-space data using a regularization framework. However, the widely used regularizations in the current CS methods often lead to smoothing effects and thus are unable to reconstruct the coronary vessel walls with sufficient resolution. To address this issue, a novel block-weighted total variation regularization is presented to accelerate the coronary vessel wall MR imaging. The proposed regularization divides the image into two parts: a region-of-interest (ROI) which contains the coronary vessel wall, and the other region with less concerned features. Different penalty weights are given to the two regions. As a result, the small details within ROI do not suffer from over-smoothing while the noise outside the ROI can be significantly suppressed. Results with both numerical simulations and in vivo experiments demonstrated that the proposed method can reconstruct the coronary vessel wall from undersampled k-space data with higher qualities than the conventional CS with the total variation or the edge-preserved total variation.

Cone‐beam CT (CBCT) has been widely used in image guided radiation therapy (IGRT) to acquire updated volumetric anatomical information before treatment fractions for accurate patient alignment purpose. However the excessive x‐ray imaging doses (a few cGy per scan) delivered to patients from serial CBCT scans raise a clinical concern in most IGRT procedures. This fact has greatly limited exploitation of IGRT's maximal potential. The imaging dose can be effectively reduced by reducing the number of x‐ray projections and/or lowering mAs levels in a CBCT scan. The image quality reconstructed from conventional FDK‐type algorithms however will be highly degraded. Recently total variation (TV) method has demonstrated its ability to reconstruct CBCT images from a few number of noisy x‐ray projections. Nonetheless such a method can hardly be applied in real clinical environments due to its long computational time (a few hours). It is highly desirable to develop a fast reconstruction scheme to obtain high quality CBCT images from undersampled and noisy projection data so as to lower the imaging dose.Utilizing GPU to speed up the computationally intensive tasks in CBCT reconstruction problems has drawn a lot of attention recently. In this talk GPU‐based CBCT reconstruction algorithms will be reviewed with an emphasis on an iterative CBCT reconstruction algorithm via TV regularization. We have recently developed a GPU‐friendly version of the forward‐backward splitting algorithm to solve the TV‐based reconstruction problem. Multi‐grid technique is also employed. It is found that 40 x‐ray projections are sufficient to reconstruct CBCT images with satisfactory quality for IGRT patient alignment purpose. Phantom studies indicate that CBCT images can be successfully reconstructed with our algorithm under as low as 0.1 mAs/projection level. Comparing with currently widely used full‐fan head‐and‐neck scanning protocol of about 360 projections with 0.4 mAs/projection it is estimated that an overall 36 times dose reduction has been achieved. Moreover the reconstruction time is about 130 sec on an NVIDIA Tesla C1060 GPU card which is estimated ∼100 times faster than similar iterative reconstruction approaches. The high computational efficiency and satisfactory image quality make the iterative low dose CBCT reconstruction approach feasible in real clinical environments.Learning Objectives:1. Understand basic concepts of GPU‐based CBCT reconstruction.2. Understand main challenges in GPU‐based iterative CBCT reconstruction approach and how an iterative CBCT reconstruction problem is solved on GPU.Conflict of Interest: The research presented here is partially supported by NVIDIA.

To develop a phase encoding reduction scheme based on compressed sensing (CS) for phase-encoded (1) H MR spectroscopic imaging (MRSI). Phantom and in vivo rat brain MRSI experiments were performed at 7 Tesla to examine the performance of CS approach and compare it with the full k-space acquisition. The CS undersampling was performed by acquiring a pseudorandom and density-varying subset of phase encodings. Residual water resonance was first removed from the undersampled k-space dataset before CS reconstruction. The CS reconstruction was performed by a linearized Bregman iteration procedure for efficiency in computing large scale L1 minimization. The spectral and spatial fidelity was evaluated by comparing spectral linewidths and metabolite maps and voxel-wise Bland-Altman analysis. CS preserved the spectral resolution and metabolite content levels. No spectral broadening was observed, and the estimation biases of the metabolite content levels were no more than 4%. CS clearly preserved the boundaries of metabolite maps but led to slight loss of details in metabolite maps. This study demonstrated the feasibility of the proposed CS approach to accelerate phase-encoded (1) H MRSI.

Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations of the imaging process. In the past decades, total variation regularization played a dominant role in the literature. Two forms of total variation regularizations, namely the first-order and the second-order total variation (TV-1 and TV-2) have been widely used. TV-1 has a disadvantage: it reconstructs images in the form of piece-wise constants when the noise and/or under-sampling is severe, while TV-2 reconstructs natural-looking images under such scenarios. On the other hand, TV-1 can recover sharp jumps better than TV-2. Two forms of generalizations, namely Hessian-Schatten norm (HSN) regularization, and total generalized variation (TGV) regularization, have been proposed and have become significant developments in the area of regularization for imaging inverse problems owing to their performance. While the strength of TGV is that it can combine the advantages of TV-1 and TV-2, HSN has better structure-preserving property. Here, we develop a novel regularization for image recovery that combines the strengths of TGV and HSN. We achieve this by restricting the maximization space in the dual form of HSN in the same way that TGV is obtained from TV-2. We call the new regularization the generalized Hessian-Schatten norm regularization (GHSN). We develop a novel computational method for image reconstruction using the new form of regularization based on the well-known framework called the alternating direction method of multipliers (ADMM). We demonstrate the strength of the GHSN using some reconstruction examples.

We introduce a total variation (TV) regularization model for synthetic aperture radar (SAR) image despeckling. A dual-formulation-based adaptive TV (ATV) regularization method is applied to solve the TV regularization. The parameter adaptation of the TV regularization is performed based on the noise level estimated via wavelets. The TV-regularization-based image restoration model has a good performance in preserving image sharpness and edges while removing noises, and it is therefore effective for edge preserve SAR image despeckling. Experiments have been carried out using optical images contaminated with artificial speckles first and then SAR images. A despeckling evaluation index (DEI) is designed to assess the effectiveness of edge preserve despeckling on SAR images, which is based on the ratio of the standard deviations of two neighborhood areas of different sizes of a pixel. Experimental results show that the proposed ATV method can effectively suppress SAR image speckles without compromising the edge sharpness of image features according to both subjective visual assessment of image quality and objective evaluation using DEI.

Purpose:To develop a novel reconstruction method for X‐ray CT that can lead to accurate reconstruction at significantly reduced dose levels combining low X‐ray incident intensity and few views of projection data.Methods:The noise nature of the projection data at low X‐ray incident intensity was modeled and accounted by the weighted least‐squares (WLS) criterion. The total variation (TV) penalty was used to mitigate artifacts caused by few views of data. The first order primal‐dual (FOPD) algorithm was used to minimize TV in image domain, which avoided the difficulty of the non‐smooth objective function. The TV penalized WLS reconstruction was achieved by alternated FOPD TV minimization and projection onto convex sets (POCS) for data fidelity constraints. The proposed FOPD‐POCS method was evaluated using the FORBILD jaw phantom and the real cadaver head CT data.Results:The quantitative measures, root mean square error (RMSE) and contrast‐to‐noise ratio (CNR), demonstrate the superior denoising capability of WLS over LS‐based TV iterative reconstruction. The improvement of RMSE (WLS vs. LS) is 15%∼21% and that of CNR is 17%∼72% when the incident counts per ray are ranged from 1×105 to 1×103. In addition, the TV regularization can accurately reconstruct images from about 50 views of the jaw phantom. The FOPD‐POCS reconstruction reveals more structural details and suffers fewer artifacts in both the phantom and real head images. The FOPD‐POCS method also shows fast convergence at low X‐ray incident intensity.Conclusion:The new hybrid FOPD‐POCS method, based on TV penalized WLS, yields excellent image quality when the incident X‐ray intensity is low and the projection views are limited. The reconstruction is computationally efficient since the FOPD minimization of TV is applied only in the image domain. The characteristics of FOPD‐POCS can be exploited to significantly reduce radiation dose of X‐ray CT without compromising accuracy for diagnosis or treatment planning.

To solve the ill-posed problem in electrical impedance tomography (EIT) and overcome the blur effect made by conventional L2 Tikhonov regularization, a new two-step iterative regularization algorithm is applied for the process reconstruction of lung respiration. This algorithm is based on total variation (TV) regularization method, and uses a two-step iterative method with TV denoising operator, so that it can achieve double regularization effect. This algorithm has advantages in both resolution and robustness. Both simulation and experiment results are executed to prove the effectiveness of TV regularization method.

ABSTRACTThis study newly demonstrates a compressed sensing (CS)-based reconstruction scheme for computed tomography (CT) with a translational trajectory. CT with a translational trajectory has many potential applications in the field of non-destructive testing (NDT) and medicine. For example, in the X-ray inspection of a large civil engineering structure, the movements of the source and detector are strictly limited, and a simple straight CT trajectory is preferable. This method could also be applied in X-ray inspection lines in factories and airports. In the medical field, this method would complement the tomosynthesis in mammography. When using a translational trajectory, the dispersion of the fan- or cone-beam creates projection data with the angular information of the sample object. However, the angular information inevitably becomes insufficient when using a translational trajectory, which degrades the reconstruction accuracy. In this case, CS is considered suitable for reconstruction because it has been successfully used for reconstructions from sparse-view and limited-angle data. For reconstruction from the translational trajectory projection, a new concept of directional difference (DD) regularization was proposed. An algorithm was developed based on the alternating direction method of multipliers (ADMM) algorithm to solve the regularization problem. Numerical reconstruction experiments from noisy projection data were conducted and the results were compared with those from other reconstruction methods. The convergence performance of the total variation (TV), DD, and mixed TV-DD regularization methods were examined. The proposed DD and TV-DD methods showed better performance than the TV only regularization. Reconstruction from Monte-Carlo simulated projection data was also demonstrated.

It is required that input features are represented as vectors or scalars in machine learning for classification, e.g. support vector machine (SVM). However, real world data such as 2D images is naturally represented as matrices or tensors with higher dimensions. Thus, structural information of the data whose dimensions are more than two is not successfully considered. One typical structural information which is useful for the classification task is the spatial relationship of the nearby data points. In this paper, to leverage this kind of structural information, we propose a novel classification method which combines total variational (TV) regularization with SVM, called TV-SVM. Since TV achieves a local smoothing property by penalizing the local discontinuity of data, TV-SVM preserves better local structure than the original SVM due to TV regularization. We solve the objective function of TV-SVM via the alternating direction method of multipliers (ADMM) algorithm. Experimental results on image classification show that TV-SVM is competitive to the state-of-the-art learning method in both classification accuracy and computational complexity.

This study develops an improved Feldkamp–Davis–Kress (FDK) reconstruction algorithm using non-local total variation (NLTV) denoising and a cubic B-spline interpolation-based backprojector to enhance the image quality of low-dose cone-beam computed tomography (CBCT). The NLTV objective function is minimized on all log-transformed projections using steepest gradient descent optimization with an adaptive control of the step size to augment the difference between a real structure and noise. The proposed algorithm was evaluated using a phantom data set acquired from a low-dose protocol with lower milliampere-seconds (mAs).The combination of NLTV minimization and cubic B-spline interpolation rendered the enhanced reconstruction images with significantly reduced noise compared to conventional FDK and local total variation with anisotropic penalty. The artifacts were remarkably suppressed in the reconstructed images. Quantitative analysis of reconstruction images using low-dose projections acquired from low mAs showed a contrast-to-noise ratio with spatial resolution comparable to images reconstructed using projections acquired from high mAs. The proposed approach produced the lowest RMSE and the highest correlation. These results indicate that the proposed algorithm enables application of the conventional FDK algorithm for low mAs image reconstruction in low-dose CBCT imaging, thereby eliminating the need for more computationally demanding algorithms. The substantial reductions in radiation exposure associated with the low mAs projection acquisition may facilitate wider practical applications of daily online CBCT imaging.

Efficient general sparse denoising with non-convex sparse constraint and total variation regularization

In this paper, we present a novel method of computing tomography , i.e. the low third deviation total variation (LTD-TV) method to reconstruct the two-dimensional distribution of SO<sub>2</sub> of stack plume. The path-integral data of the plume are collected by only two imaging differential absorption spectrometers (IDOASs). However, due to the insufficient number of IDOASs, conventional reconstruction methods result in severe streaking artifacts. The traditional low third derivative method is widely used to reconstruct the gas distribution. It suggests a spatial distribution of gas concentrations, which has a low third spatial derivative in every direction and at every point. The derivatives are usually set to be zero. The method improves the reconstructed images by providing extra information which contains the gas concentration in line with the distribution of the second order polynomial, but it also gives rise to the extra artifacts. To address this issue, we further improve the traditional low third deviation (LTD) method by suggesting that the third derivative of gas concentration is sparse. We therefore adopt the compressed sensing (CS) based total variation (TV) optimization framework. In the LTD-TV method, a logarithmic barrier function with TV is used as an objective function. The objective function is then optimized by numerical optimization method, in which the gradient projection is used to determine its descent direction and a Barzilai-Borwein scheme to determine its step-size. The final results are obtained by iterative optimization. Numerical simulations are performed to simulate the reconstruction of gas distribution which is in line with Gaussian distribution. Compared with the conventional LTD method, the LTD-TV method enhances the proximity by 20%—80%, and greatly corrects the artifacts near the edges of images. The result of field campaign suggests that concordance correlation factor between the collected data and reconstructed image is 0.9023. It also shows that it has good noise immunity. In summary, it is the first time that we have introduced the CS theory into the field of gas plume reconstruction. Compared with the existing methods, the LTD-TV method can greatly reduce the artifacts and increase the credibility of the reconstruction.