Research On Measurement Matrix For Compressive Sensing

Compressive sensing (CS) is a new sampling framework for acquisition and processing of signals. The signals have the characteristics of sparsity and compressibility, thus the high dimensional signals can be accurately or approximately reconstructed through non-related measurement of sampling signals in low dimension. During the process of CS, measurement matrix plays an important role in data sampling and signal reconstruction. Therefore, the research on measurement matrix for CS is very significant. In this paper, we focus on the research of the measurement matrix, and the main work of this paper is as follows:Firstly, we constructed the measurement matrix based on the chaotic sequences. Comparing with other techniques, chaotic system generates the pseudo-random matrix with better randomness. Moreover, it is easy to be generated and implemented by physical electric circuit. Therefore, we attempt to construct the measurement matrix with several common discrete chaotic sequences. Some experiments, are taken on one-dimensional time-domain sparse signal, one-dimensional frequency-domain sparse signal and two-dimensional images, to compare the performance of the proposed method with random Gaussian measurement matrix and random Bernoulli measurement matrix. Meanwhile the simulation results show that the chaotic measurement matrix out performs the other random measurement matrixes on both objective evaluation guidelines and visual effect.Secondly, we proposed a self-adaptive block compressive sampling scheme for images based on pulsed contourlet cosine transform (PCOT). Typically, compressive sensing of images is block by block, where image acquisition is conducted in a block-by-block manner using the same sampling ratio. According to the CS theory, a reconstruction algorithm would offer better reconstruction quality of an image block with more measurements. However, it has shown that the perceptual quality of image is largely influenced by visual attention, and human vision would pay more attention to the salient regions of an image but less attention to the rest of the image. Thus, this approach is not reasonable because it assigns the same sampling ratio for all the blocks, whose contents can vary significantly across different patches or blocks. To solve this problem, a pulsed contourlet cosine transform is used to locate the visual salient areas. Moreover, we allocate more sensing resources to salient attention areas but fewer to non-salient attention areas in compressive sampling. Some experiments are taken on images show that the proposed scheme improves the quality of reconstructed image remarkably compared to the case when saliency information is not used on both objective evaluation index and visual effect.Finally, we proposed a self-adaptive block compressive sampling scheme for images based on multi-scale support value transform (MSVT). Based on the self-adaptive block compressive sampling scheme, we use multi-scale support value transform to obtain the salient information of image. According to this salient information, both the salient attention regions and the non-salient attention regions can be efficiently determined. Meanwhile, more sensing resources are allocated to salient attention areas but fewer to non-salient attention regions, then the signal reconstruction algorithm can recover all the image blocks from the self-adaptive sampling data. Some experiments are taken to compare the performance of our proposed scheme with the case when saliency information is not used and some other related saliency detection approaches. The simulation results show that the new scheme can obtain higher quality of recovered images than the self-adaptive block compressive sampling scheme for images based PCOT, especially in preserving the edges, contours and complex structures at the same sampling ratio as that of uniform sampling.This paper was supported by the National Science Foundation of China (under Grant No.61072108,60601029,60971112,61173090), the Program for New Century Excellent Talents in University (under Grant No. NCET-10-0668), the Program of Introducing Talents of Discipline to Universities (the111Project, under Grant No.B0704) and the Basic Science Research Fund in University Supported by Central Government (under Grant No. JY10000902041).