Adaptive Fast Composite Splitting Algorithm for MR Image Reconstruction

Compressed Sensing (CS) exploits sparsity of images to reconstruct them exactly from a small set of measurements. Recent studies have shown that nonlocal sparsity leads to superior results in CS recovery. In this paper, we first propose a new sparsity model, which is characterized as a function of the coefficients achieved by transforming the 3D array generated from a set of similar image patches. The function which we use is the nonconvex Garrote function. To efficiently solve the proposed corresponding optimization problem, we then employ an accelerated algorithm based on iterative proximal methods. Our reconstruction method exploits the benefits of both nonlocal sparsity and nonconvex optimization. Experimental results show effectiveness of the proposed method compared with the many existing algorithms in CS image recovery.

This paper proposes an adaptive reconstruction method for parallel imaging (PI) via sparse representation over a learned dictionary and also a corresponding dictionary learning based PI (DL-PI) algorithm. DL-PI adopts the "divide and conquer" strategy to solve the ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -DL reconstruction formulation, with dictionary learning to capture the structure information and a Taylor approximation to update the target image analytically. The proposed approach has been applied to parallel magnetic resonance imaging (MRI) and compared to two latest state-of-the-art methods. The experimental results on in-vivo data show that the DL-PI algorithm possesses strong ability in detail preservation and is competent in artifact removal during the MR image reconstruction process.

Accelerated magnetic resonance imaging techniques reduce signal acquisition time by undersampling k-space. A fundamental problem in accelerated magnetic resonance imaging is the recovery of quality images from undersampled k-space data. Current state-of-the-art recovery algorithms exploit the spatial and temporal structures in underlying images to improve the reconstruction quality. In recent years, compressed sensing theory has helped formulate mathematical principles and conditions that ensure recovery of (structured) sparse signals from undersampled, incoherent measurements. In this article, a new recovery algorithm, motion-adaptive spatio-temporal regularization, is presented that uses spatial and temporal structured sparsity of MR images in the compressed sensing framework to recover dynamic MR images from highly undersampled k-space data. In contrast to existing algorithms, our proposed algorithm models temporal sparsity using motion-adaptive linear transformations between neighboring images. The efficiency of motion-adaptive spatio-temporal regularization is demonstrated with experiments on cardiac magnetic resonance imaging for a range of reduction factors. Results are also compared with k-t FOCUSS with motion estimation and compensation-another recently proposed recovery algorithm for dynamic magnetic resonance imaging. .

Low-dose computed tomography (CT) has attracted much attention in clinical applications since X-ray radiations can cause serious health risks to patients. Sparse-view CT imaging is one of the major ways to reduce radiation dose. However, if reconstructing the sparse-view CT images with conventional filtered backprojection (FBP) algorithm, image quality may be significantly degraded due to the severe streaking artifacts. Therefore, iterative sparse-view CT image reconstruction (IR) algorithms have been developed and utilized to improve image quality. One drawback of using the IR algorithms is they usually spend long computation time. Additionally, adjusting and optimizing the hyper-parameters that are needed during iteration procedures is also time-consuming, some- times may even depend on individual experience. These potential drawbacks strongly limit the wide applications of IR algorithms. Aiming at partially overcome such difficulties, in the present work, we propose a deep iterative reconstruction (DIR) framework to generalize the conventional IR algorithms by mapping them into the deep neural network (DNN) technique. With this proposed DIR algorithms, the prior term, the data fidelity term, and the hyper-parameters can all be represented and learned by network. By doing so, some generalized iterative models can be used to perform high quality sparse-view CT image reconstructions. Numerical experiments based on clinical patient data demonstrated that the proposed DIR algorithms can mitigate the streaking artifacts more effectively while well preserving the subtle structures.

BackgroundThe challenge of reconstructing a sparse medical magnetic resonance image based on compressed sensing from undersampled k-space data has been investigated within recent years. As total variation (TV) performs well in preserving edge, one type of approach considers TV-regularization as a sparse structure to solve a convex optimization problem. Nevertheless, this convex optimization problem is both nonlinear and nonsmooth, and thus difficult to handle, especially for a large-scale problem. Therefore, it is essential to develop efficient algorithms to solve a very broad class of TV-regularized problems.MethodsIn this paper, we propose an efficient algorithm referred to as the fast linearized preconditioned alternating direction method of multipliers (FLPADMM), to solve an augmented TV-regularized model that adds a quadratic term to enforce image smoothness. Because of the separable structure of this model, FLPADMM decomposes the convex problem into two subproblems. Each subproblem can be alternatively minimized by augmented Lagrangian function. Furthermore, a linearized strategy and multistep weighted scheme can be easily combined for more effective image recovery.ResultsThe method of the present study showed improved accuracy and efficiency, in comparison to other methods. Furthermore, the experiments conducted on in vivo data showed that our algorithm achieved a higher signal-to-noise ratio (SNR), lower relative error (Rel.Err), and better structural similarity (SSIM) index in comparison to other state-of-the-art algorithms.ConclusionsExtensive experiments demonstrate that the proposed algorithm exhibits superior performance in accuracy and efficiency than conventional compressed sensing MRI algorithms.

In photoacoustic tomography (PAT), imaging speed is an essential metricthat is restricted by the pulse laser repetition rate and the numberof channels on the data acquisition card (DAQ). Reconstructing theinitial sound pressure distribution with fewer elements cansignificantly reduce hardware costs and back-end acquisition pressure.However, undersampling will result in artefacts in the photoacousticimage, degrading its quality. Dictionary learning (DL) has beenutilised for various image reconstruction techniques, but theydisregard the uniformity of pixels in overlapping blocks. Therefore,we propose a compressive sensing (CS) reconstruction algorithm forcircular array PAT based on gradient domain convolutional sparsecoding (CSCGR). A small number of non-zero signal positions in thesparsely encoded feature map are used as partially known support (PKS)in the reconstruction procedure. The CS-CSCGR-PKS-based reconstructionalgorithm can use fewer ultrasound transducers for signal acquisitionwhile maintaining image fidelity. We demonstrated the effectiveness ofthis algorithm in sparse imaging through imaging experiments on themouse torso, brain, and human fingers. Reducing the number of arrayelements while ensuring imaging quality effectively reduces equipmenthardware costs and improves imaging speed.

Synthetic aperture radar (SAR) is widely used for ground observations owing to its all-weather and all-time capabilities. Sparse SAR reconstruction imaging, which can enhance SAR imaging performance, has emerged as a significant research area. The traditional sparse SAR reconstruction imaging method was successfully applied to raw SAR data processing. However, the computational complexity makes sparse reconstruction imaging difficult for large scenes. Meanwhile, because raw data are usually kept confidential, only limited data are available. To address the issue of how to use publicly available complex image data for sparse reconstruction and effectively improve image quality, this study proposes a joint L1- and F-norm edge-preservation-based sparse SAR reconstruction algorithm for complex images. The algorithm uses the gradient descent (GD) technique to optimize the L1-norm regularization and reconstruct the overall image information; the iterative soft thresholding algorithm (ISTA) to optimize the F-norm regularization and reconstruct the high-frequency image information; and fuses the two sets of reconstructed information to obtain SAR reconstructed images with characteristics such as edge preservation, clear texture, and high quality. The results show that, compared with traditional matched filtering (MF) imaging results, the joint L1- and F-norm results obtained for complex images have lower sidelobes, higher signal-to-noise ratio, and better target resolution ability; compared with the F-norm-based sparse SAR reconstruction imaging results, the joint L1- and F-norm method provides images with better edge texture clarity.

Many state-of-the-art denoising algorithms often employ dictioanary learning methods to acquire the mapping relationship between the polluted image by noise and the original clean image. It is critical to generate the appropriate dictionary in image de noising based on dictionary learning. In order to promote the de noising efficiency, the proposed algorithm employs Online Dictionary Learning (ODL) to train the overcomplete dictionaries to make the dictionary more accurate. The dictionary updating procedure is improved with a warm start. The dictionary is updated by the last computed dictionary and the current input image patches. Hence the dictionary is more accurate to get better denoising images. In the experiments, the PSNR of ODL dictionary is 0.12dB higher than SCDL and 0.21dB higher than K-SVD in average. The proposed method can eliminate the artifacts and recover the texture details efficiently.

Denoising algorithms via sparse representation are among the state-of-the art for 2D image restoration. In this work, we propose a novel sparse and prior-based algorithm for 3D image denoising (SPADE). SPADE is a modification of total variation (TV) problem with an additional functional that promotes sparsity with respect to a prior image. The prior is obtained from the noisy image by combining information from neighbor slices. The functional is minimized using the split Bregman method, which leads to an efficient method for large scale 3D denoising, with computational cost given by three FFT per iteration. SPADE is compared to TV and dictionary learning on the Shepp-Logan phantom and on human knee data acquired on a spectral computerized tomography scanner. SPADE converges in approximately ten iterations and provides comparable or better results than the other methods. In addition, the exploitation of the prior image avoids the patchy, cartoon-like images provided by TV and provides a more natural texture.

In seismic data processing, denoising is crucial for identifying the Earth’s subsurface structure. Erratic noise in seismic data is challenging because of its high amplitude and non-Gaussian distribution characteristics. Dictionary learning with KSVD requires a longer computational time due to its iterative nature at various stages. To address this, we propose a robust denoising DHHL method that utilises mini-batch dictionary learning, the quantum Harrow–Hassidim–Lloyd (HHL) algorithm, and quantum singular value transformation (QSVT) to attenuate random and erratic noise in seismic data. The HHL algorithm provides a significant estimate of the sparse coefficient. The HHL provides a theoretically efficient method for sparse coding with favorable asymptotic scaling, improving the potential scalability of the method. Mini-batch dictionary learning constructs hierarchical dictionaries, thereby enhancing the capture of signal features in seismic data. QSVT enables the direct transformation of singular values, leading to faster convergence and more accurate sparse representations for dictionary updating. Here, we use minimisation loss using ℓ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> to provide group sparsity and preserve the signal features. The proposed DHHL method was applied to both synthetic and field datasets. The efficiency of the DHHL method was assessed using evaluation metrics such as the signal-to-noise ratio (SNR), mean squared error (MSE), and local similarity map. The quantitative and visual results indicate that the DHHL method achieved a higher SNR, minimised the MSE with less signal leakage, and reduced the computational time by accelerating sparse coding.

Developing accurate models and efficient representations of multivariate trajectories is important for understanding the behavior patterns of mobile agents. This work presents a dictionary learning algorithm for developing a part-based trajectory representation, which combines merits of the existing Markovian-based and clustering-based approaches. In particular, this work presents the augmented semi-nonnegative sparse coding (ASNSC) algorithm for solving a constrained dictionary learning problem, and shows that the proposed method would converge to a local optimum given a convexity condition. We consider a trajectory modeling application, in which the learned dictionary atoms correspond to local motion patterns. Classical semi-nonnegative sparse coding approaches would add dictionary atoms with opposite signs to reduce the representational error, which can lead to learning noisy dictionary atoms that correspond poorly to local motion patterns. ASNSC addresses this problem and learns a concise set of intuitive motion patterns. ASNSC shows significant improvement over existing trajectory modeling methods in both prediction accuracy and computational time, as revealed by extensive numerical analysis on real datasets.

Group-based sparse representation for image compressive sensing reconstruction with non-convex regularization

This paper introduces an efficient algorithm for magnetic resonance (MR) image reconstruction. The proposed method minimizes a linear combination of nonlocal total variation and least-square data-fitting term to reconstruct the MR images from undersampled k-space data. The nonlocal total variation is taken as the L 1-regularization functional and solved using Split Bregman iteration. The proposed algorithm is compared with previous methods in terms of the reconstruction accuracy and computational complexity. The comparison results demonstrate the superiority of the proposed algorithm for compressed MR image reconstruction.

Multi-energy computed tomography (MECT) based on a photon-counting detector is an emerging imaging modality that collects projections at several energy bins with a single scan. However, the limited number of photons collected into the divided, narrow energy bins results in high quantum noise levels in reconstructed images. This study aims to improve MECT image quality by minimizing noise levels while retaining image details. A novel MECT reconstruction method was proposed by exploiting the nonlocal tensor similarity among interchannel images and spatial sparsity in single-channel images. Similar patches were initially extracted from the interchannel images in spectral and spatial domains, then stacked into a new three-order tensor. Intrinsic tensor sparsity regularization that combined the Tuker and canonical polyadic (CP) low-rank decomposition techniques were applied to exploit the nonlocal similarity of the formulated tensor. Spatial sparsity in single-channel images was modeled by total variation (TV) regularization that utilizes the compressibility of gradient image. A new MECT reconstruction model was established by simultaneously incorporating the intrinsic tensor sparsity and TV regularizations. The iterative alternating minimization method was utilized to solve the reconstruction model based on a flexible framework. The proposed method was applied to the digital phantom and real mouse data to assess its feasibility and reliability. The reconstruction and decomposition results in the mouse data were encouraging and demonstrated the ability of the proposed method in noise suppression while preserving image details, not observed with other methods. Imaging data from the digital phantom illustrated this method as achieving the best intuitive reconstruction and decomposition results among all compared methods. They reduced the root mean square error (RMSE) by 89.75%, 50.75%, and 36.54% on the reconstructed images compared with analytic, TV-based, and tensor-based methods, respectively. This phenomenon was also observed with decomposition results, where the RMSE was also reduced by 97.96%, 67.74%, 72.05%, respectively. In this study, we proposed a reconstruction method for photon counting detector-based MECT, using the intrinsic tensor sparsity and TV regularizations. Improvements in noise suppression and detail preservation in the digital phantom and real mouse data were validated by the qualitative and quantitative evaluations on the reconstruction and decomposition results, verifying the potential of the proposed method in MECT reconstruction.

To improve the magnetic resonance imaging (MRI) data acquisition speed while maintaining the reconstruction quality, a novel method is proposed for multislice MRI reconstruction from undersampled k-space data based on compressed-sensing theory using dictionary learning. There are two aspects to improve the reconstruction quality. One is that spatial correlation among slices is used by extending the atoms in dictionary learning from patches to blocks. The other is that the dictionary-learning scheme is used at two resolution levels; i.e., a low-resolution dictionary is used for sparse coding and a high-resolution dictionary is used for image updating. Numerical experiments are carried out on in vivo 3D MR images of brains and abdomens with a variety of undersampling schemes and ratios. The proposed method (dual-DLMRI) achieves better reconstruction quality than conventional reconstruction methods, with the peak signal-to-noise ratio being 7 dB higher. The advantages of the dual dictionaries are obvious compared with the single dictionary. Parameter variations ranging from 50% to 200% only bias the image quality within 15% in terms of the peak signal-to-noise ratio. Dual-DLMRI effectively uses the a priori information in the dual-dictionary scheme and provides dramatically improved reconstruction quality.