Segmented compressive sensing

Abstract

This paper presents an alternative way of random sampling of signals/images in the framework of compressed sensing. In spite of usual random samplers which take p measurements from the input signal, the proposed method uses M different samplers each taking p i (i = 1, 2, 3 . . . M) samples. Therefore, the overall number of samples will be q = Mp . Using this method a variable sampling criterion based on the content of the segments is achievable. Following this idea, the calculated measurement (or sensing) matrix is also more incoherent in columns comparing to other conventional methods which is a desired feature. Our experiments show that the reconstructed signal using this method has a better SNR and is more robust compared to the systems using one sampler.

An adaptive orthogonal matching pursuit algorithm based on redundancy dictionary

“…However, a large sample size means less efficient in the compression, so the size should be minimized. Literature [10] applied the segmented compressed sensing (SCS) [4] idea to block compressed sensing [12] (BCS) and proposed a method that can reduce the sample size. This method can adaptively adjust the sample size with the high reconstruction quality in image reconstruction.…”

“…In 2006, Candès and Donoho et al proposed Compressed Sensing [1,2,3,4,5] sampling theories based on the signal sparsity which changed the way of sampling signals. Currently many mature signal reconstruction algorithms have been proposed, such as the minimum l 1 norm Basis Pursuit [6] (BP) algorithm which can effectively achieve the linear reconstruction, but its computational complexity is high.…”

A Novel Measurement Matrix Optimization Approach for Hyperspectral Unmixing

“…Design of measurement matrix is a research hotspot in CS, and measurement matrix optimization has become an inevitable trend to construct a new measurement matrix system. In recent years, scholars have yielded many optimization methods [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] to design measurement matrix to reduce the minimum coherence of Gram matrix. These are typically fallen into three categories: iterative thresholding method [3][4][5][6][7][8][9][10][11][12][13][14], gradient iteration process [15][16][17][18][19], and Tensor product [20][21][22].…”

Guided compressive sensing single-pixel imaging technique based on hierarchical model

“…In general, sensing matrix is set as random. Nevertheless, some authors recently attempted to determine an optimal structure for sensing matrix (explicitly or implicitly) to increase the reconstruction quality and take fewer measurements to complete such process [8][9][10][11][12][13]. Elad et al [8] tried to iteratively decrease the average mutual coherence in sensing matrix by adopting a shrinkage operation followed by a singular value decomposition step.…”

“…Elad et al [8] tried to iteratively decrease the average mutual coherence in sensing matrix by adopting a shrinkage operation followed by a singular value decomposition step. In [9], the authors applied a kind of nonuniform sampling by segmenting the input signal and taking samples with different rates from each segment. In [10], which explored the magnetic resonance imaging, the authors described an incoherence criterion based on point spread function and proposed a Monte Carlo scheme for random incoherent sampling for this kind of data.…”