Designing robust sensing matrix for image compression

Abstract

This paper deals with designing sensing matrix for compressive sensing systems. Traditionally, the optimal sensing matrix is designed so that the Gram of the equivalent dictionary is as close as possible to a target Gram with small mutual coherence. A novel design strategy is proposed, in which, unlike the traditional approaches, the measure considers of mutual coherence behavior of the equivalent dictionary as well as sparse representation errors of the signals. The optimal sensing matrix is defined as the one that minimizes this measure and hence is expected to be more robust against sparse representation errors. A closed-form solution is derived for the optimal sensing matrix with a given target Gram. An alternating minimization-based algorithm is also proposed for addressing the same problem with the target Gram searched within a set of relaxed equiangular tight frame Grams. The experiments are carried out and the results show that the sensing matrix obtained using the proposed approach outperforms those existing ones using a fixed dictionary in terms of signal reconstruction accuracy for synthetic data and peak signal-to-noise ratio for real images.

Optimized structured sparse sensing matrices for compressive sensing

“…where the first term is utilized to control the average mutual coherence of the equivalent dictionary, the second term Φ E 2 F is a regularization to make the sensing matrix robust to SRE, and λ ≥ 0 is the trade-off parameter to balance these two terms. Compared with previous work, simulations have shown that the obtained sensing matrices by (7) achieve the highest signal recovery accuracy when the SRE exists [14].…”

“…Towards that end, it is important to develop a quantized (even 1-bit) sparse sensing matrix. We finally note that it remains an open problem to certify certain properties (such as the RIP) for the optimized sensing matrices [9][10][11][12][13][14][15][16][17][18][19], which empirically outperforms a random one that satisfies the RIP. Works in these directions are ongoing.…”

“…Although random matrices satisfy the RIP with high probability [7], confirming whether a general matrix satisfies the RIP is NP-hard [8]. Alternatively, mutual coherence, another measure of sensing matrices that is much easier to verify, has been introduced in practice to quantify and design sensing matrices [9][10][11][12][13][14][15][16][17][18][19].…”

A preconditioning approach for improved estimation of sparse polynomial chaos expansions

“…Similar issue exists for designing a projection (or sensing) matrix in signal processing application. Recent studies have proposed to design a projection matrix such that it improves incoherence properties of equivalent dictionary, and its multiplication by the noise vector results in a vector with small magnitude [38,39,40]. However, it's more challenging to design a preconditioning matrix for an underdetermined regression problem as both sides of the equation, Ψc+e = u, are multiplied by the preconditioning matrix.…”

Greedy Algorithm for Image Compression in Image Processing

“…In the event that the compressed image is decompressed then it will be identical to the original image. There are various lossless image compression techniques are Run length encoding, Huffman encoding, Area coding, Data folding [7]. Mansour Nejati, et.al, (2016) proposed in this paper [8] a boosted dictionary learning structure to develop an ensemble of complementary particular dictionaries for sparse image representation.…”