Simple algorithm for
            <i>L</i>
            1‐norm regularisation‐based compressed sensing and image restoration

Qin, Shun

doi:10.1049/iet-ipr.2020.0194

Cited by 7 publications

(6 citation statements)

References 29 publications

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“…where the sparsity of the vector Yx encouraged by the l 1 norm (Qin, 2020). In addition, the common idea of network-based CS method is to replace the operators in traditional CS methods with neural networks (Liu et al, 2021).…”

Section: Cs Reconstruction Methodsmentioning

confidence: 99%

ESPC-BCS-Net: A network-based CS method for underwater image compression and reconstruction

Chen²,

Yu³

2023

Front. Mar. Sci.

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The Internet of Underwater Things (IoUT) is a typical energy-limited and bandwidth-limited system where the technical bottleneck is the asymmetry between the massive demand for information access and the limited communication bandwidth. Therefore, storing and transmitting high-quality underwater images is a challenging task. The data measured by cameras need to be effectively compressed before transmission to reduce storage and reconstruc-ted with minor errors, which is the best solution. Compressed sensing (CS) theory breaks through the Nyquist sampling theorem and has been widely used to reconstruct sparse signals accurately. For adaptive sampling underwater images and improving the reconstruction performance, we propose the ESPC-BCS-Net by combining the advantages of CS and Deep Learning. The ESPC-BCS-Net consists of three parts: Sampling-Net, ESPC-Net, and BCS-Net. The parameters (e.g. sampling matrix, sparse transforms, shrinkage thresholds, etc.) in ESPC-BCS-Net are learned end-to-end rather than hand-crafted. The Sampling-Net achieves adaptive sampling by replacing the sampling matrix with a convolutional layer. The ESPC-Net implements image upsampling, while the BCS-Net is used to image reconstruction. The efficient sub-pixel layer of ESPC-Net effectively avoids blocking artifacts. The visual and quantitative evaluation of the experimental results shows that the underwater image reconstruction still performs well when the CS ratio is 0.1 and the PSNR of the reconstructed underwater images is above 29.

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Section: Cs Reconstruction Methodsmentioning

confidence: 99%

ESPC-BCS-Net: A network-based CS method for underwater image compression and reconstruction

Chen²,

Yu³

2023

Front. Mar. Sci.

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“…The regularized model approach investigated both the TV norm (as provided above) and the L 1 norm 16,17 as penalty terms. The L 1 norm is defined as…”

Section: Indirect Solutionsmentioning

confidence: 99%

“…The regularized model approach investigated both the

TV

norm (as provided above) and the

L_1

norm 16,17 as penalty terms. The

L_1

norm is defined as

\begin{equation*} \Vert x\Vert _1 = \sum _{i=1}^n |[x]_i|.

…”

Section: Introductionmentioning

confidence: 99%

Superiorization versus regularization: A comparison of algorithms for solving image reconstruction problems with applications in computed tomography

et al. 2021

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A system matrix can be built in order to account for the refractions in an optical computed tomography (CT) system. In order to utilize this system matrix, iterative methods are employed to solve the image reconstruction problem. The purpose of this study is to compare potential iterative algorithms to solve this image reconstruction problem. Comparisons examine both solution time and the quality of the reconstructed image. While our work is motivated by optical CT, the results can be extended more generally to CT. Methods: A collection of 21 algorithms for solving the image reconstruction problem were evaluated. Specifically, algorithms using (i) superiorization techniques and (ii) regularization to avoid overfitting were compared. Multiple test problems are investigated using 18 different image phantoms, parallel-beam and fan-beam system matrices, and varying noise levels. Comparison of the algorithms is done using performance profiles on three different performance measures. Results:The results for both the synthetic and clinical test problems show that there is not one single algorithm outperforming all others, but instead a set of top algorithms that give the best values on the performance profiles. When qualitative analyses such as reliance on stopping conditions, number of input parameters, and run time are also considered, FISTA-TV shows slight advantages over the other top algorithms. Conclusions: There is a set of top algorithms that all show good results in the performance profiles with a mix of superiorized and regularized model algorithms. As to which of these top algorithms outperforms the rest is undetermined and further research needs to be investigated.

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“…The first term in Equation ( 7) is the matrix regression loss function. Inspired by the basic idea of sparse regression for feature selection in [8], the sparse matrix regression (SMR) model can be obtained by replacing the Frobenius norm in the second term of the function (7) with the L 2,1 -norm: min…”

Section: Matrix Regression (Mr)mentioning

confidence: 99%

“…Zhang et al [6] claimed that the collaborative representation strategy plays a more important role than the L 1 -norm based sparsity constraint by analyzing the working mechanism of SRC and proposed a collaborative representation-based classification (CRC). Qin [7] relaxed the L 1 -norm regularized optimization problem to a non-linear optimization problem with L 1 -norm approximation by a smoothening function, which can be solved by existing powerful non-linear optimization methods. Nie et al [8] present a robust linear regression model based on sparse constraints and design a robust feature selection (RFS) algorithm.…”

Section: Introductionmentioning

confidence: 99%

Low‐rank nonnegative sparse representation and local preservation‐based matrix regression for supervised image feature selection

Zhu

Chen

2021

IET Image Processing

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Matrix regression has attracted much attention due to directly select some meaningful features from matrix data. However, most existing matrix regressions do not consider the global and local structure of the matrix data simultaneously. To this end, we propose a lowrank nonnegative sparse representation and local preserving matrix regression (LNSRLP-MR) model for image feature selection. Here, the loss function is defined by the left and right regression matrices. To capture the global structure and discriminative information of the training images and reduce the effect of heterogeneous data and noises, we impose the low-rank constraint on the self-representation error matrix and the nonnegative sparse constraint on the coefficient vector. The graph matrix can be learned adaptively through representation coefficients, so that accurate local structure information in samples can be revealed. Feature selection is performed by obtained row sparse transformation matrix. An optimization procedure and its performance are also present. Experimental results on several image datasets show that compared with the-state-of-the-art method, the average classification accuracy of the proposed method is improved by at least 1.2% and up to 3.3%. For images with noise or occlusion, the accuracy is improved significantly, up to 4%, which indicates that this method has strong robustness.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Simple algorithm for L 1‐norm regularisation‐based compressed sensing and image restoration

Cited by 7 publications

References 29 publications

ESPC-BCS-Net: A network-based CS method for underwater image compression and reconstruction

ESPC-BCS-Net: A network-based CS method for underwater image compression and reconstruction

Superiorization versus regularization: A comparison of algorithms for solving image reconstruction problems with applications in computed tomography

Low‐rank nonnegative sparse representation and local preservation‐based matrix regression for supervised image feature selection

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