Optimized Projection Matrix for Compressive Sensing

Abstract

Compressive sensing (CS) is mainly concerned with low-coherence pairs, since the number of samples needed to recover the signal is proportional to the mutual coherence between projection matrix and sparsifying matrix. Until now, papers on CS always assume the projection matrix to be a random matrix. In this paper, aiming at minimizing the mutual coherence, a method is proposed to optimize the projection matrix. This method is based on equiangular tight frame (ETF) design because an ETF has minimum coherence. It is impossible to solve the problem exactly because of the complexity. Therefore, an alternating minimization type method is used to find a feasible solution. The optimally designed projection matrix can further reduce the necessary number of samples for recovery or improve the recovery accuracy. The proposed method demonstrates better performance than conventional optimization methods, which brings benefits to both basis pursuit and orthogonal matching pursuit.

Compressive sensing using optimized sensing matrix for face verification

“…From the results, it showed that the optimized sensing matrix based on equiangular tight frame [6]can be improved the performance of face verification system using compressive sensing. Future improvements can be done by considering the noise in verifying a face so that the system can be implemented in practice also communication between client and server can be developed further so that it can communicate via the internet.…”

“…However, the sensing matrix can further be optimized by minimizing the averaged mutual coherence of the equivalent dictionary. In this paper,sensing matrix optimization algorithms based on equiangular tight frame [6] is used. Fig.…”

“…1 describes the process of face verification system using compressive sensing with optimized sensing matrix. Discrete cosine transform is used as dictionary and sensing matrix used in CS process in client laptop or reconstruction in server laptop is random sensing matrix with addition of a key and has go through the optimization process using algorithm in [6]. It needs to send request to server laptop to send dictionary as in the client la ptop does not have dictionary.…”

“…Based on research that has been done before [4], the level of accuracy obtained from non-optimized systems reached more than 80% and for optimized is able to reach more than 90%. In this research, by comparing Gradient Descent used previous research [5] with different sensing matrix optimization algorithms based on equiangular tight frame [6] but uses two kinds of sparse coding, namely Orthogonal Matching Pursuit (OMP) [7] which is the same as the previous research and IRLS-ℓp for comparison that is expected to reach a better level of accuracy [8].…”

One-step-ahead kinematic compressive sensing

“…The method iteratively reduces large elements in the Gram matrix A T A directly, and then computes a new projection satisfying rank conditions associated with the desired number of measurements. Duarte-Carvajalino and Sapiro [7] addressed the same objective shortly thereafter as an eigenstructure problem, and achieved faster computations; Xu et al [8] followed with an approach based on the equiangular tight frame, and reported further improvements, although computing times are not given. These methods put no constraints on P and the outcome of optimization is dense in the general case, because implicit is the assumption that all of y is available.…”