scholarly journals Gradient Projection with Approximate L0 Norm Minimization for Sparse Reconstruction in Compressed Sensing

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3373 ◽  
Author(s):  
Ziran Wei ◽  
Jianlin Zhang ◽  
Zhiyong Xu ◽  
Yongmei Huang ◽  
Yong Liu ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Objective Function ◽  
Signal Reconstruction ◽  
Reconstruction Error ◽  
Sparse Signal ◽  
Reconstruction Accuracy ◽  
L1 Norm ◽  
Function Model ◽  
L2 Norm

In the reconstruction of sparse signals in compressed sensing, the reconstruction algorithm is required to reconstruct the sparsest form of signal. In order to minimize the objective function, minimal norm algorithm and greedy pursuit algorithm are most commonly used. The minimum L1 norm algorithm has very high reconstruction accuracy, but this convex optimization algorithm cannot get the sparsest signal like the minimum L0 norm algorithm. However, because the L0 norm method is a non-convex problem, it is difficult to get the global optimal solution and the amount of calculation required is huge. In this paper, a new algorithm is proposed to approximate the smooth L0 norm from the approximate L2 norm. First we set up an approximation function model of the sparse term, then the minimum value of the objective function is solved by the gradient projection, and the weight of the function model of the sparse term in the objective function is adjusted adaptively by the reconstruction error value to reconstruct the sparse signal more accurately. Compared with the pseudo inverse of L2 norm and the L1 norm algorithm, this new algorithm has a lower reconstruction error in one-dimensional sparse signal reconstruction. In simulation experiments of two-dimensional image signal reconstruction, the new algorithm has shorter image reconstruction time and higher image reconstruction accuracy compared with the usually used greedy algorithm and the minimum norm algorithm.

Signal Reconstruction Based on a Fusion Compressed Sensing Frame

2013 ◽  
Vol 785-786 ◽  
pp. 1315-1323
Author(s):  
Xu Hua Li ◽  
Yue Li Chen ◽  
Nan Jun Hu ◽  
Wei Li ◽  
Tian Jun Yuan ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Matching Pursuit ◽  
Signal To Noise Ratio ◽  
Signal Reconstruction ◽  
Greedy Algorithms ◽  
Reconstruction Error ◽  
Reconstruction Accuracy ◽  
Support Sets ◽  
Reconstruction Effects ◽  
Better Than

Greedy algorithms represented by orthogonal matching pursuit (OMP) and subspace pursuit (SP) algorithms are practically used in image processing based upon compressed sensing theory. However, there are two disadvantages: 1)Relatively poor signal reconstruction accuracy; 2) High computation complexity and measurements time. This paper proposes a frame of greedy algorithms obtaining a novel fusion of matching pursuit (FMP), combining the OMP and SP algorithms. FMP unites the two support sets from OMP and SP selecting the most appropriate atoms to achieve secondary screening of the original two support sets, finally realizing the accurate signal reconstruction. Using same test conditions, image reconstruction experiments and stability of Frame, the proposed FMP algorithm can effectively improve signal-to-noise ratio (SNR) with improved reconstruction error. Reconstruction effects using proposed FMP are better than separately using other two greedy algorithms for both high and low resolution images.

Distributed Compressed Sensing Based Channel Parameter Estimation for MIMO-FBMC Communications

2021 ◽  
Author(s):  
Han Wang ◽  
Xianpeng Wang
Keyword(s):  
Channel Estimation ◽  
Compressed Sensing ◽  
Signal Reconstruction ◽  
Estimation Method ◽  
Sparse Signal ◽  
Weak Selection ◽  
Sparse Signal Reconstruction ◽  
Distributed Compressed Sensing ◽  
Time Frequency ◽  
Selection Threshold

Abstract For the sparse correlation between channels in multiple input multiple output filter bank multicarrier with offset quadrature amplitude modulation (MIMO-FBMC/OQAM) systems, the distributed compressed sensing (DCS)-based channel estimation approach is studied. A sparse adaptive distributed sparse channel estimation method based on weak selection threshold is proposed. Firstly, the correlation between MIMO channels is utilized to represent a joint sparse model, and channel estimation is transformed into a joint sparse signal reconstruction problem. Then, the number of correlation atoms for inner product operation is optimized by weak selection threshold, and sparse signal reconstruction is realized by sparse adaptation. The experiment results show that proposed DCS-based method not only estimates the multipath channel components accurately but also achieves higher channel estimation performance than classical orthogonal matching pursuit (OMP) method and other traditional DCS methods in the time-frequency dual selective channels.

Adaptive Dual Conjudate Gradient Projection Algorithm for Compressed Sensing Image Reconstruction

2013 ◽  
Vol 347-350 ◽  
pp. 2600-2604
Author(s):  
Hai Xia Yan ◽  
Yan Jun Liu
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Sparse Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Accuracy ◽  
Reconstruction Quality ◽  
Dual Gradient

In order to improve the quality of noise signals reconstruction method, an algorithm of adaptive dual gradient projection for sparse reconstruction of compressed sensing theory is proposed. In ADGPSR algorithm, the pursuit direction is updated in two conjudate directions, the better original signals estimated value is computed by conjudate coefficient. Thus the reconstruction quality is improved. Experiment results show that, compared with the GPSR algorithm, the ADGPSR algorithm improves the signals reconstruction accuracy, improves PSNR of reconstruction signals, and exhibits higher robustness under different noise intensities.

Rapid Gradient Projection Algorithm for Image Reconstruction

2014 ◽  
Vol 530-531 ◽  
pp. 443-446
Author(s):  
Hai Xia Yan ◽  
Yan Jun Liu
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Gradient Descent ◽  
Target Function ◽  
Reconstruction Algorithm ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Descent Direction ◽  
Reconstruction Accuracy ◽  
Gradient Projection Algorithm

In order to improve the speed of compressed sensing image reconstruction algorithm, a rapid gradient projection algorithm for image reconstruction is proposed. In traditional Gradient Projection algorithm, the pursuit direction is alternating, in rapid gradient projection algorithm, we use the Newton's method to calculate the gradient descent direction, thus the constraints conditions of gradient projection is satisfied. And the target function is updated in each iteration computing. The effect of approximation matrix to target function is reduced. The iteration computing times is reduced, because the algorithm works in accurate search direction. Experiment results show that, compared with the GPSR algorithm, the RGPSR algorithm improves the signals reconstruction accuracy, improves PSNR of reconstruction signals, and exhibits higher robustness under different noise intensities.

scholarly journals Tree-Based Backtracking Orthogonal Matching Pursuit for Sparse Signal Reconstruction

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yigang Cen ◽  
Fangfei Wang ◽  
Ruizhen Zhao ◽  
Lihong Cui ◽  
Lihui Cen ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Optimization Problem ◽  
Selection Process ◽  
Matching Pursuit ◽  
Signal Reconstruction ◽  
Search Space ◽  
Orthogonal Matching Pursuit ◽  
Superior Performance ◽  
Sparse Signal ◽  
Tree Model

Compressed sensing (CS) is a theory which exploits the sparsity characteristic of the original signal in signal sampling and coding. By solving an optimization problem, the original sparse signal can be reconstructed accurately. In this paper, a new Tree-based Backtracking Orthogonal Matching Pursuit (TBOMP) algorithm is presented with the idea of the tree model in wavelet domain. The algorithm can convert the wavelet tree structure to the corresponding relations of candidate atoms without any prior information of signal sparsity. Thus, the atom selection process will be more structural and the search space can be narrowed. Moreover, according to the backtracking process, the previous chosen atoms’ reliability can be detected and the unreliable atoms can be deleted at each iteration, which leads to an accurate reconstruction of the signal ultimately. Compared with other compressed sensing algorithms, simulation results show the proposed algorithm’s superior performance to that of several other OMP-type algorithms.

scholarly journals l1- andl2-Norm Joint Regularization Based Sparse Signal Reconstruction Scheme

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Chanzi Liu ◽  
Qingchun Chen ◽  
Bingpeng Zhou ◽  
Hengchao Li
Keyword(s):  
Signal Reconstruction ◽  
Reconstruction Error ◽  
Gradient Algorithm ◽  
Sparse Signal ◽  
Reconstruction Problem ◽  
Sparse Signal Reconstruction ◽  
Linear System Of Equations ◽  
Sparse Solution ◽  
Application Condition ◽  
New Formulation

Many problems in signal processing and statistical inference involve finding sparse solution to some underdetermined linear system of equations. This is also the application condition of compressive sensing (CS) which can find the sparse solution from the measurements far less than the original signal. In this paper, we proposel1- andl2-norm joint regularization based reconstruction framework to approach the originall0-norm based sparseness-inducing constrained sparse signal reconstruction problem. Firstly, it is shown that, by employing the simple conjugate gradient algorithm, the new formulation provides an effective framework to deduce the solution as the original sparse signal reconstruction problem withl0-norm regularization item. Secondly, the upper reconstruction error limit is presented for the proposed sparse signal reconstruction framework, and it is unveiled that a smaller reconstruction error thanl1-norm relaxation approaches can be realized by using the proposed scheme in most cases. Finally, simulation results are presented to validate the proposed sparse signal reconstruction approach.

scholarly journals Compressed Sensing Based Dynamic MR Image Reconstruction By Using 3D-Total Generalized Variation and Tensor Decomposition: k-t TGV-TD

2021 ◽  
Author(s):  
Jucheng Zhang ◽  
Lulu Han ◽  
Jianzhong Sun ◽  
Zhikang Wang ◽  
Wenlong Xu ◽  
...  
Keyword(s):  
Magnetic Resonance ◽  
Image Reconstruction ◽  
Compressed Sensing ◽  
Sparse Representation ◽  
Tensor Decomposition ◽  
Low Rank ◽  
Reconstruction Accuracy ◽  
Mr Image ◽  
Cardiac Mr ◽  
Mr Image Reconstruction

Abstract Purpose: Compressed Sensing Magnetic Resonance Imaging (CS-MRI) is a promising technique to accelerate dynamic cardiac MR imaging (DCMRI). For DCMRI, the CS-MRI usually exploits image signal sparsity and low-rank property to reconstruct dynamic images from the undersampled k-space data. In this paper, a novel CS algorithm is investigated to improve dynamic cardiac MR image reconstruction quality under the condition of minimizing the k-space recording.Methods: The sparse representation of 3D cardiac magnetic resonance data is implemented by synergistically integrating 3D TGV algorithm and high order singular value decomposition (HOSVD) based Tensor Decomposition, termed as k-t TGV-TD method. In the proposed method, the low rank structure of the 3D dynamic cardiac MR data is performed by the HOSVD method, and the localized image sparsity is achieved by the 3D TGV method. Moreover, the Fast Composite Splitting Algorithm (FCSA) method, combining the variable splitting with operator splitting techniques, is employed to solve the low-rank and sparse problem. Two different cardiac MR datasets (cardiac cine and cardiac perfusion MR data) are used to evaluate the performance of the proposed method.Results: Compared with the state-of-art methods, such as the k-t SLR method, 3D TGV method and HOSVD based tensor decomposition method, the proposed method can offer improved reconstruction accuracy in terms of higher signal-to-error ratio (SER).Conclusions: This work proved that the k-t TGV-TD method was an effective sparse representation way for DC-MRI, which was capable of significantly improving the reconstruction accuracy with different reduction factor.

Improved Gradient Projection Algorithm for Compressed Sensing

2014 ◽  
Vol 543-547 ◽  
pp. 2623-2626
Author(s):  
Hai Xia Yan ◽  
Yan Jun Liu
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Reconstruction Accuracy ◽  
Gradient Projection Algorithm ◽  
Gradient Direction ◽  
Searching Method ◽  
Negative Gradient

In order to improve efficient of compressed sensing image reconstruction, an improved gradient projection algorithm of compressed sensing theory is proposed. In improved Gradient Projection algorithm, the pursuit direction is updated by search at negative gradient direction, thus the gradient direction is a single direction, because the traditional gradient projection algorithm searching at alternating searching method ,the efficient of gradient projection algorithm is higher than the traditional gradient projection algorithm, Experiment results show that, compared with the GPSR algorithm, the IGPSR algorithm improves the signals reconstruction accuracy, improves PSNR of reconstruction signals, and exhibits higher robustness under different noise intensities.

scholarly journals Inverse Synthetic Aperture Radar Sparse Imaging Exploiting the Group Dictionary Learning

2021 ◽  
Vol 13 (14) ◽  
pp. 2812
Author(s):  
Changyu Hu ◽  
Ling Wang ◽  
Daiyin Zhu ◽  
Otmar Loffeld
Keyword(s):  
Image Reconstruction ◽  
Dictionary Learning ◽  
Reconstruction Error ◽  
Imaging Method ◽  
L1 Norm ◽  
Norm Minimization ◽  
Imaging Results ◽  
Computational Speed ◽  
Feature Information ◽  
The Relationship

Sparse imaging relies on sparse representations of the target scenes to be imaged. Predefined dictionaries have long been used to transform radar target scenes into sparse domains, but the performance is limited by the artificially designed or existing transforms, e.g., Fourier transform and wavelet transform, which are not optimal for the target scenes to be sparsified. The dictionary learning (DL) technique has been exploited to obtain sparse transforms optimized jointly with the radar imaging problem. Nevertheless, the DL technique is usually implemented in a manner of patch processing, which ignores the relationship between patches, leading to the omission of some feature information during the learning of the sparse transforms. To capture the feature information of the target scenes more accurately, we adopt image patch group (IPG) instead of patch in DL. The IPG is constructed by the patches with similar structures. DL is performed with respect to each IPG, which is termed as group dictionary learning (GDL). The group oriented sparse representation (GOSR) and target image reconstruction are then jointly optimized by solving a l1 norm minimization problem exploiting GOSR, during which a generalized Gaussian distribution hypothesis of radar image reconstruction error is introduced to make the imaging problem tractable. The imaging results using the real ISAR data show that the GDL-based imaging method outperforms the original DL-based imaging method in both imaging quality and computational speed.

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