In this letter, a construction of sparse measurement matrices is presented. Based on finite fields, a base matrix is obtained. Then a Hadamard matrix or a discrete Fourier transform (DFT) matrix is nested in the base matrix, which eventually formes a new deterministic measurement matrix. The coherence of the proposed matrices is low, which meets the Welch bound asymptotically. Thus these matrices could satisfy the restricted isometry property (RIP). Simulation results demonstrate that the proposed matrices give better performance than Gaussian counterparts.

In compressive sensing theory (CS), the restricted isometry property (RIP) is commonly used for the measurement matrix to guarantee the reliable recovery of sparse signals from linear measurements. Although many works have indicated that random matrices with excellent recovery performance satisfy the RIP with high probability, Toeplitz-structured matrices arise naturally in real scenarios, such as applications of linear time-invariant systems. Thus, the corresponding measurement matrix can be modeled as a Toeplitz (partial) structured matrix instead of a completely random matrix. The structure characteristics introduce coherence and cause the performance degradation of the measurement matrix. To enhance the recovery performance of the Toeplitz structured measurement matrix in multichannel convolution source separation, an efficient construction of measurement matrix is presented, referred to as sparse random block-banded Toeplitz matrix (SRBT). The sparse signal is pre-randomized by locally scrambling its sample locations. Then, the signal is subsampled using the sparse random banded matrix. Finally, the mixing measurements are obtained. Based on the analysis of eigenvalues, the theoretical results indicate that the SRBT matrix satisfies the RIP with high probability. Simulation results show that the SRBT matrix almost matches the recovery performance of random matrices. Compared with the existing banded block Toeplitz matrix, SRBT significantly improves the probability of successful recovery. Additionally, SRBT has the advantages of low storage requirements and fast computation in reconstruction.

Compressed Sensing based CMOS image sensor (CS-CIS) is a new generation of CMOS image sensor that significantly reduces the power consumption. For CS-CIS, the image quality and data volume of output are two important issues to concern. In this paper, we first proposed an algorithm to generate a series of deterministic and ternary matrices, which improves the image quality, reduces the data volume and are compatible with CS-CIS. Proposed matrices are derived from the approximate DCT and trimmed in 2D-zigzag order, thus preserving the energy compaction property as DCT does. Moreover, we proposed matrix row operations adaptive to the proposed matrix to further compress data (measurements) without any image quality loss. At last, a low-cost VLSI architecture of measurements compression with proposed matrix row operations is implemented. Experiment results show our proposed matrix significantly improve the coding efficiency by BD-PSNR increase of 4.2 dB, comparing with the random binary matrix used in the-state-of-art CS-CIS. The proposed matrix row operations for measurement compression further increases the coding efficiency by 0.24 dB BD-PSNR (4.8% BD-rate reduction). The VLSI architecture is only 4.3 K gates in area and 0.3 mW in power consumption.

This paper presents a measurement-domain intra prediction coding framework that is compatible with compressive sensing (CS)-based image sensors. In this framework, we propose a low-complexity intra prediction algorithm that can be directly applied to measurements captured by the image sensor. We proposed a structural random 0/1 measurement matrix, embedding the block boundary information that can be extracted from the measurements for intra prediction. Furthermore, a low-cost Very Large Scale Integration (VLSI) architecture is implemented for the proposed framework, by substituting the matrix multiplication with shared adders and shifters. The experimental results show that our proposed framework can compress the measurements and increase coding efficiency, with 34.9% BD-rate reduction compared to the direct output of CS-based sensors. The VLSI architecture of the proposed framework is 9.1 Kin area, and achieves the 83% reduction in size of memory bandwidth and storage for the line buffer. This could significantly reduce both the energy consumption and bandwidth in communication of wireless camera systems, which are expected to be massively deployed in the Internet of Things (IoT) era.

The information maximization (Infomax) based on information entropy theory is a class of methods that can be used to blindly separate the sources. Torkkola applied the Infomax criterion to blindly separate the mixtures where the sources have been delayed with respect to each other. Compared to the frequency domain methods, this time domain method has simple adaptation rules and can be easily implemented. However, Torkkola's method works only in the real valued field. In this letter, the Infomax for blind separation of the delayed sources is extended to the complex case for processing of complex valued signals. Firstly, based on the gradient ascent the adaptation rules for the parameters of the unmixing network are derived and the steps of algorithm are given. Then, a measurement matrix is constructed to evaluate the separation performance. The results of computer experiment support the extended algorithm.

In compressed sensing, the design of the measurement matrix is a key work. In order to achieve a more precise reconstruction result, the columns of the measurement matrix should have better orthogonality or linear incoherence. A random matrix, like a Gaussian random matrix (GRM), is commonly adopted as the measurement matrix currently. However, the columns of the random matrix are only statistically-orthogonal. By substituting an orthogonal basis into the random matrix to construct a semi-random measurement matrix and by optimizing the mutual coherence between dictionary columns to approach a theoretical lower bound, the linear incoherence of the measurement matrix can be greatly improved. With this optimization measurement matrix, the signal can be reconstructed from its measures more precisely.