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.

A Differential Evolution Algorithm for Multi-objective Sparse Reconstruction

2021 ◽  
Vol 01 ◽  
Author(s):  
Xiaopei Zhu ◽  
Li Yan ◽  
Boyang Qu ◽  
Pengwei Wen ◽  
Zhao Li
Keyword(s):  
Differential Evolution ◽  
Signal Reconstruction ◽  
Differential Evolution Algorithm ◽  
Magnetic Resonance Images ◽  
Sparse Signal ◽  
Sparse Reconstruction ◽  
Reconstruction Problem ◽  
Sparse Signal Reconstruction ◽  
Multi Objective ◽  
Evolution Algorithm

Aims: This paper proposes a differential evolution algorithm to solve the multi-objective sparse reconstruction problem (DEMOSR). Background: The traditional method is to introduce the regularization coefficient and solve this problem through a regularization framework. But in fact, the sparse reconstruction problem can be regarded as a multi-objective optimization problem about sparsity and measurement error (two contradictory objectives). Objective: A differential evolution algorithm to solve multi-objective sparse reconstruction problem (DEMOSR) in sparse signal reconstruction and the practical application. Methods: First of all, new individuals are generated through tournament selection mechanism and differential evolution. Secondly, the iterative half thresholding algorithm is used for local search to increase the sparsity of the solution. To increase the diversity of solutions, a polynomial mutation strategy is introduced. Results: In sparse signal reconstruction, the performance of DEMOSR is better than MOEA/D-ihalf and StEMO. In addition, it can verify the effectiveness of DEMOSR in practical applications for sparse reconstruction of magnetic resonance images. Conclusions: According to the experimental results of DEMOSR in sparse signal reconstruction and the practical application of reconstructing magnetic resonance images, it can be proved that DEMOSR is effective in sparse signal and image reconstruction.

A Randomized Framework for Estimating Image Saliency Through Sparse Signal Reconstruction

2018 ◽  
Vol 9 (2) ◽  
pp. 1-20
Author(s):  
Kui Fu ◽  
Jia Li
Keyword(s):  
Prior Knowledge ◽  
Signal Reconstruction ◽  
Ground Truth ◽  
Saliency Map ◽  
Reconstruction Error ◽  
Sparse Signal ◽  
Sparse Signal Reconstruction ◽  
Image Saliency ◽  
Mental Map ◽  
The Subject

This article proposes a randomized framework that estimates image saliency through sparse signal reconstruction. The authors simulate the measuring process of ground-truth saliency and assume that an image is free-viewed by several subjects. In the free-viewing process, each subject attends to a limited number of regions randomly selected, and a mental map of the image is reconstructed by using the subject-specific prior knowledge. By assuming that a region is difficult to be reconstructed will become conspicuous, the authors represent the prior knowledge of a subject by a dictionary of sparse bases pre-trained on random images and estimate the conspicuity score of a region according to the activation costs of sparse bases as well as the sparse reconstruction error. Finally, the saliency map of an image is generated by summing up all conspicuity maps obtained. Experimental results show proposed approach achieves impressive performance in comparisons with 16 state-of-the-art approaches.

scholarly journals Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs

2021 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Minh N. Dao ◽  
Guoyin Li
Keyword(s):  
Optimization Problems ◽  
Model Problem ◽  
Signal Reconstruction ◽  
Stationary Points ◽  
Sparse Signal ◽  
Reconstruction Problem ◽  
Scale Invariant ◽  
Sparse Signal Reconstruction ◽  
Fractional Programs ◽  
Subgradient Algorithm

In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, which encompass many important modern optimization problems arising from diverse areas such as the recently proposed scale-invariant sparse signal reconstruction problem in signal processing. We propose a proximal subgradient algorithm with extrapolations for solving this optimization model and show that the iterated sequence generated by the algorithm is bounded and that any one of its limit points is a stationary point of the model problem. The choice of our extrapolation parameter is flexible and includes the popular extrapolation parameter adopted in the restarted fast iterative shrinking-threshold algorithm (FISTA). By providing a unified analysis framework of descent methods, we establish the convergence of the full sequence under the assumption that a suitable merit function satisfies the Kurdyka–Łojasiewicz property. Our algorithm exhibits linear convergence for the scale-invariant sparse signal reconstruction problem and the Rayleigh quotient problem over spherical constraint. When the denominator is the maximum of finitely many continuously differentiable weakly convex functions, we also propose another extrapolated proximal subgradient algorithm with guaranteed convergence to a stronger notion of stationary points of the model problem. Finally, we illustrate the proposed methods by both analytical and simulated numerical examples.

Smoothing inertial neurodynamic approach for sparse signal reconstruction via Lp-norm minimization

2021 ◽  
Vol 140 ◽  
pp. 100-112
Author(s):  
You Zhao ◽  
Xiaofeng Liao ◽  
Xing He ◽  
Rongqiang Tang ◽  
Weiwei Deng
Keyword(s):  
Signal Reconstruction ◽  
Sparse Signal ◽  
Sparse Signal Reconstruction ◽  
Lp Norm ◽  
Norm Minimization

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.

Underdetermined DOA Estimation for Wideband Signals via Joint Sparse Signal Reconstruction

2019 ◽  
Vol 26 (10) ◽  
pp. 1541-1545 ◽  
Author(s):  
Yunmei Shi ◽  
Xing-Peng Mao ◽  
Chunlei Zhao ◽  
Yong-Tan Liu
Keyword(s):  
Signal Reconstruction ◽  
Doa Estimation ◽  
Sparse Signal ◽  
Sparse Signal Reconstruction ◽  
Wideband Signals
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