Faster Maximum Feasible Subsystem solutions for dense constraint matrices

Firouzeh, Fereshteh Fakhar; Chinneck, John W.; Rajan, Sreeraman

doi:10.1016/j.cor.2021.105633

Cited by 2 publications

(1 citation statement)

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“…All these methods need many iterations to obtain the solution. In [109], the authors subtly modify the iteration process of finding the largest cardinality feasible subset of an infeasible set of linear constraints by merging two loops into one and provides early exit conditions. They apply the modified algorithm on sparse recovery in compressive sensing that greatly increase the speed while preserving solution quality, but it still needs iterations.…”

Section: Improve Efficiency Of Traditional Cs Methods By Means Of Neu...mentioning

confidence: 99%

Reconstruction of Compressive Sensed (CS) Images with Deep Equilibrium Model (DEQ) Based on Iterative Shrinkage-Thresholding Algorithm (ISTA)

Yu¹

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Compressive sensing (CS) is a signal processing technique that measures and compresses signal simultaneously and reconstructs it by finding solutions from underdetermined linear system. CS needs much smaller number of measurements than what is required by the Nyquist-Shannon sampling theorem. Traditional optimization algorithms require many iterations to reconstruct the signal and therefore it is time consuming. Accordingly, there is a need for quicker reconstruction methods. The objective of this thesis is to explore the application of neural network in CS inverse problem to get reconstruction quickly. This thesis has four main contributions. First, we use convolutional neural network (CNN) to improve efficiency of traditional CS reconstruction for sparse signal. The nonzero positions are directly found by CNN, then the rank deficiency model is converted into a full rank model and accurate reconstruction can be solved. Second, for the compressible signal such as image, we develop the semi-tensor product (STP) into a neural network. The measurement matrix is much smaller than that of traditional CS. The proposed STP-Net makes the sampling process convenient and provides good initial reconstruction without block artifacts. Third, inspired by iterative shrinkage-thresholding algorithm (ISTA), we build SPT-ISTA-Net. The model incorporates aggregated residual transformations (ResNeXt) to promote performance improvement and a squeeze-and-excitation (SE) block to enhance useful information. Fourth, to simplify the model structure, we built a deep equilibrium model dubbed as STP-DEQ-Net. The model uses one ISTA block as an implicit layer to implement an arbitrarily deep network. The model has competitive performance, and it has a trade-off between accuracy and computation. Multi-scale dilated convolutional layers are used to further improve performance.

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Section: Improve Efficiency Of Traditional Cs Methods By Means Of Neu...mentioning

confidence: 99%