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

Compressive sensing (CS) is widely being used in recent times for image compression and transmission. The major challenge in CS is perfect reconstruction of the original image from fewest samples with fast convergence. Dictionary learning and the wide-ranging optimization problem give rise to high computation complexity. Group sparse representation (GSR)-based approach is one of the fast and efficient methods of CS image recovery. However, it may tend to oversmoothen the recovered image. This research work focuses on enhancing the performance of GSR-based methods. In this research work, both local and non-local image patches are exploited in two phases of reconstruction. In the initialization phase, adaptive sparsifying l0 optimization model is utilized for local overlapping patches. Further, constrained GSR is applied on the outcome. The split Bregman iteration is harnessed to solve the resultant patch-group model. The execution time, PSNR and FSIM are employed as the evaluation parameters for evaluating the CS performance. The parametric performance is tested over a set of standard images. The experimental results show the competence of the proposed patch-group method over the existing ALSB, GSR and GSR-NCR (GSR with non-convex regularization) methods. The proposed model offers 1.3, 0.32 and 0.51 dB average PSNR gain over ALSB, GSR and GSR-NCR methods, respectively. The average execution time taken by the proposed work is 29% less than the traditional GSR method.

A novel dictionary learning method for sparse representation with nonconvex regularizations

In remote sensing applications and medical imaging, one of the key points is the acquisition, real-time preprocessing and storage of information. Due to the large amount of information present in the form of images or videos, compression of these data is necessary. Compressed sensing is an efficient technique to meet this challenge. It consists in acquiring a signal, assuming that it can have a sparse representation, by using a minimum number of nonadaptive linear measurements. After this compressed sensing process, a reconstruction of the original signal must be performed at the receiver. Reconstruction techniques are often unable to preserve the texture of the image and tend to smooth out its details. To overcome this problem, we propose, in this work, a compressed sensing reconstruction method that combines the total variation regularization and the non-local self-similarity constraint. The optimization of this method is performed by using an augmented Lagrangian that avoids the difficult problem of nonlinearity and nondifferentiability of the regularization terms. The proposed algorithm, called denoising-compressed sensing by regularization (DCSR) terms, will not only perform image reconstruction but also denoising. To evaluate the performance of the proposed algorithm, we compare its performance with state-of-the-art methods, such as Nesterov’s algorithm, group-based sparse representation and wavelet-based methods, in terms of denoising and preservation of edges, texture and image details, as well as from the point of view of computational complexity. Our approach permits a gain up to 25% in terms of denoising efficiency and visual quality using two metrics: peak signal-to-noise ratio (PSNR) and structural similarity (SSIM).

Due to proper use of the image sparsity, CS (compressed sensing) image compression has made great achievements in the field of image compression without the constraint of Nyquist sampling law. A great deal of researches indicate that there exist obvious statistical and structural priors regularity for image information distribution, while traditional CS image compression algorithms only use the sparse characteristic of the image information. In this paper, we propose a CS image reconstruction algorithm based on the joint statistical and structural priors which can achieve efficient image reconstruction via a small amount of measurements. With the full use of inter-scale and intra-scale relations of the sparse coefficients, we optimize the iterative hard thresholding CS algorithm specifically by building a GSM model to constrain the local coefficients distribution statistically, and a tree model to constrain the global coefficients distribution structurally. Extensive simulations have been conducted and the results show that the proposed method has achieved a considerable promotion both on the speed and the PSNR gain of image reconstruction, compared with the traditional recovery algorithms under the same compression ratio.

Sparse representation matrix is of great significance for Compressed Sensing (CS) reconstruction accuracy. Contourlet Transform (CT) offer a much richer set of directions and shapes, and it is more effective in capturing smooth contours and geometric structures in images. While dictionaries learned by machine learning methods can represent images more effectively. In this paper, we propose a multi-level adaptive dictionary learning (DL) strategy which combines both of the above advantages. We learn sub-dictionaries of high frequency of CT by an improved K-SVD algorithm, and moreover, the stopping criteria of sparse representation stage is associated with the iteratively updated dictionaries to get an adaptive sparse constraint, which gets more effective sparse representation coefficients and then improves the dictionary updating. This approach achieves a good reconstruction accuracy of the high frequency with less CS measurement. Experiment results demonstrate that the reconstructed images using dictionaries learned by the proposed algorithm in CS have better effect.

The compressive sensing(CS) and sparse representation(SR) technique provide new way to improve the ISAR image resolution. At present, in most traditional CS and SR based ISAR imaging methods, the target is regarded as a set of isolated scattering centers. As a matter of fact, adjacent scattering centers compose a lot of small sets which can reflect the structure of the target. It is no doubt that these small sets can be exploited to improve the ISAR image quality, but the traditional CS and SR ISAR imaging methods ignore this. So in this paper, a block sparse signal recovery algorithm-Block Sparse Bayesian Learning(BSBL) method is introduced to modify the traditional method, and the simulate experiment show that this method can get better ISAR image than the other methods.

Blind image deconvolution, i.e., estimating both the latent image and the blur kernel from the only observed blurry image, is a severely ill-posed inverse problem. In this paper, we propose a blur kernel estimation method for blind motion deblurring using sparse representation and cross-scale self-similarity of image patches as priors to recover the latent sharp image from a single blurry image. Sparse representation indicates that image patches can always be represented well as a sparse linear combination of atoms in an appropriate dictionary. Cross-scale self-similarity results in that any image patch can in some way be well approximated by a number of other similar patches across different image scales. Our method is based on the observations that almost any image patch in a natural image has multiple similar patches in down-sampled versions of the image, and down-sampling produces image patches that are sharper than those in the blurry image itself. In our method, the dictionary for sparse representation is trained adaptively from sharper patches sampled from the down-sampled latent image estimate to make the similar patches of the latent sharp image well represented sparsely, and meanwhile, all patches from the latent image estimate are optimized to be as close to the sharper similar patches searched from the down-sampled version to enforce the sharp recovery of the latent image by constructing a non-local regularization. Experimental results on both simulated and real blurry images demonstrate that our method outperforms state-of-the-art blind deblurring methods.

To demonstrate the feasibility of compressed sensing (CS) to accelerate the acquisition of hyperpolarized (HP) 129 Xe multi-b diffusion MRI for quantitative assessments of lung microstructural morphometry. Six healthy subjects and six chronic obstructive pulmonary disease (COPD) subjects underwent HP 129 Xe multi-b diffusion MRI (b=0, 10, 20, 30, and 40s/cm2 ). First, a fully sampled (FS) acquisition of HP 129 Xe multi-b diffusion MRI was conducted in one healthy subject. The acquired FS dataset was retrospectively undersampled in the phase encoding direction, and an optimal twofold undersampled pattern was then obtained by minimizing mean absolute error (MAE) between retrospective CS (rCS) and FS MR images. Next, the FS and CS acquisitions during separate breath holds were performed on five healthy subjects (including the above one). Additionally, the FS and CS synchronous acquisitions during a single breath hold were performed on the sixth healthy subject and one COPD subject. However, only CS acquisitions were conducted in the rest of the five COPD subjects. Finally, all the acquired FS, rCS and CS MR images were used to obtain morphometric parameters, including acinar duct radius (R), acinar lumen radius (r), alveolar sleeve depth (h), mean linear intercept (Lm ), and surface-to-volume ratio (SVR). The Wilcoxon signed-rank test and the Bland-Altman plot were employed to assess the fidelity of the CS reconstruction. Moreover, the t-test was used to demonstrate the effectiveness of the multi-b diffusion MRI with CS in clinical applications. The retrospective results demonstrated that there was no statistically significant difference between rCS and FS measurements using the Wilcoxon signed-rank test (P>0.05). Good agreement between measurements obtained with the CS and FS acquisitions during separate breath holds was demonstrated in Bland-Altman plots of slice differences. Specifically, the mean biases of the R, r, h, Lm , and SVR between the CS and FS acquisitions were 1.0%, 2.6%, -0.03%, 1.5%, and -5.5%, respectively. Good agreement between measurements with the CS and FS acquisitions was also observed during the single breath-hold experiments. Furthermore, there were significant differences between the morphometric parameters for the healthy and COPD subjects (P<0.05). Our study has shown that HP 129 Xe multi-b diffusion MRI with CS could be beneficial in lung microstructural assessments by acquiring less data while maintaining the consistent results with the FS acquisitions.

Recently, compressed sensing (CS) has been widely used in ground penetrating radar (GPR) imaging due to its low sampling time, high quality performance and high quality underground imaging results. There are always a large number of matrix operations involved in CS based GPR imaging process, which takes a long time. Traditionally, all scanning area was imaged by this CS imaging method. However, with the imaging scene becoming larger, the measurement matrix and the data dictionary in CS imaging model expand, which increases the time of CS-based imaging process. Thus, this paper proposes a fast CS based GPR imaging method to reduce the imaging time. Specifically, the geometric characteristics of the B-scan image can firstly be used to extract the region of interest (ROI) where the target may exist in a layered medium. Then the GPR imaging based on CS can be realized in ROI, which can reduce the imaging area and imaging time. Experimental results present that the method can effectively reduce the time of GPR imaging based on CS.

The compressed sensing (CS) theorem is a novel sampling approach that breaks through the conventional Nyquist sampling limit and brings a revolution in the field of signal processing. This article investigates the compression technique for CS hyperspectral images so as to illustrate the superiority provided by this new theorem. First, several comparative experiments are used to reveal that the drawback of prior compression techniques, designed for the data acquired by the conventional hyperspectral imaging system, is either low compression ratio or a waste of sampling resource. After a condensed analysis, we state that the CS theorem provides the probability of avoiding such defects. Then a straightforward scheme, which takes advantage of spectral correlation, is proposed to compress the CS hyperspectral images to reduce the data size further. Moreover, a flexible recovery strategy is designed to speed up the reconstruction of original bands from the corresponding CS images. The experimental results based on the actual hyperspectral images have demonstrated the efficiency of this proposed technique.

Compressive sensing (CS) theory has been applied to sparse microwave imaging in many ways that provide better performance and significantly reduce the sampling rate. However, the computational complexity of reconstruction puts strict constraint on some practical applications with large-scale problems in radar imaging. In this paper, we propose a novel fast reconstruction scheme by realizing the traditional matched filtering with CS technique, which maintains the good performance of matched filtering with a reduced number of observations. Meanwhile, a new sparse basis is formed which offers excellent potential for reducing the computational complexity in reconstruction with fast Fourier transform (FFT) and nonuniform FFT, i.e. NUFFT, where the computational complexity can decrease from to . The feasibility and efficiency of the proposed scheme are validated as well through both numerical simulations and raw data processing results.

Breakthrough results in compressive sensing (CS) have shown that high dimensional signals (vectors) can often be accurately recovered from a relatively small number of non-adaptive linear projection observations, provided that they possess a sparse representation in some basis. Subsequent efforts have established that the reconstruction performance of CS can be improved by employing additional prior signal knowledge, such as dependency in the location of the non-zero signal coefficients (structured sparsity) or by collecting measurements sequentially and adaptively, in order to focus measurements into the proper subspace where the unknown signal resides. In this paper, we examine a powerful hybrid of adaptivity and structure. We identify a particular form of structured sparsity that is amenable to adaptive sensing, and using concepts from sparse hierarchical dictionary learning we demonstrate that sparsifying dictionaries exhibiting the appropriate form of structured sparsity can be learned from a collection of training data. The combination of these techniques (structured dictionary learning and adaptive sensing) results in an effective and efficient adaptive compressive acquisition approach which we refer to as LASeR (Learning Adaptive Sensing Representations).

The aims of this study were to develop an accelerated multiparametric magnetic resonance imaging method based on 3D-quantification using an interleaved Look-Locker acquisition sequence with a T2 preparation pulse (3D-QALAS) combined with compressed sensing (CS) and to evaluate the effect of CS on the quantitative mapping, tissue segmentation, and quality of synthetic images. A magnetic resonance imaging system phantom, containing multiple compartments with standardized T1, T2, and proton density (PD) values; 10 healthy volunteers; and 12 patients with multiple sclerosis were scanned using the 3D-QALAS sequence with and without CS and conventional contrast-weighted imaging. The scan times of 3D-QALAS with and without CS were 5:56 and 11:11, respectively. For healthy volunteers, brain volumetry and myelin estimation were performed based on the measured T1, T2, and PD. For patients with multiple sclerosis, the mean T1, T2, PD, and the amount of myelin in plaques and contralateral normal-appearing white matter (NAWM) were measured. Simple linear regression analysis and Bland-Altman analysis were performed for each metric obtained from the datasets with and without CS. To compare overall image quality and structural delineations on synthetic and conventional contrast-weighted images, case-control randomized reading sessions were performed by 2 neuroradiologists in a blinded manner. The linearity of both phantom and volunteer measurements in T1, T2, and PD values obtained with and without CS was very strong (R2 = 0.9901-1.000). The tissue segmentation obtained with and without CS also had high linearity (R2 = 0.987-0.999). The quantitative tissue values of the plaques and NAWM obtained with CS showed high linearity with those without CS (R2 = 0.967-1.000). There were no significant differences in overall image quality between synthetic contrast-weighted images obtained with and without CS (P = 0.17-0.99). Multiparametric imaging of the whole brain based on 3D-QALAS can be accelerated using CS while preserving tissue quantitative values, tissue segmentation, and quality of synthetic images.

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.

Reconstruction of an image from undersampled k-space data using conventional sparsity priors use any of the pre-specified transforms like wavelet, which utilizes the global sparsity of images. Alternatively, methods such as block-matching and 3D filtering (BM3D) utilize the non-local sparsity of images, resulting in better preservation of finer details. However, use of either of the methods cannot utilize global and non-local sparsity at the same time. In this paper, we propose an efficient combination of the global and non-local sparsity realized using wavelet and BM3D, implemented using the fast composite splitting denoising (FCSD) algorithm. Furthermore, we use an adaptive regularization parameter for the wavelet to yield the best achievable performance using adaptive thresholded Landweber (ATL). The proposed adaptive fast composite splitting denoising algorithm (AFCSD) combines the advantages of both BM3D with adaptive TL through the use of FCSD and thus exploits the self-repetitive structure in images by enforcing non-local sparsity as well as entire consistency of the image. Experimental results reveal that the proposed method is superior to any of the individual methods in terms of reconstruction accuracy and computation complexity. Additionally, when used as an auxiliary constraint in dictionary learning (DL), this can result in further improvements in reconstruction with significant reduction in the computation time as compared to a conventional DL reconstruction.