Deterministic Compressed Sensing Matrices From Sequences With Optimal Correlation

Abstract

Compressed sensing (CS) is a new method of data acquisition which aims at recovering higher dimensional sparse vectors from considerably smaller linear measurements. One of the key problems in CS is the construction of sensing matrices. In this paper, we construct deterministic sensing matrices, using Zhou-Helleseth-Udaya sequences and Udaya-Siddiqi sequences. We also construct deterministic sensing matrices using quaternary sequence families A and D. With the orthogonal matching pursuit, numerical simulations show that some of our proposed sensing matrices outperform several typical known sensing matrices in terms of the rate of exact reconstruction.

Random Hybrid Chirp Sensing Matrix Implementation for Fast Compressive Sensing SAR Processing

“…특히 첩센싱 행렬식(chirp sensing matrix)은 복잡도를 기존 방식 대비 데이터 길이에 대한 로그 스케일로 줄여서 빠른 재구성이 가능하게 한 다 [7] . 대부분의 결정 센싱 행렬식은 랜덤 행렬식과 비교 하여 상대적으로 각 행 함수간의 간섭이 증가하는 코히 어런스(coherence) 성질을 가지고 있다 [8], [9] . 따라서 기존의 첩 센싱 행렬식을 사용하면 처리 시간은 단축되지만, 행 렬식 내부의 상호 간섭이 증가하여 독립성(orthogonality) 이 약해지고 결과적으로 압축센싱 알고리즘의 성능이 저 하되는 문제가 발생한다 [8], [10] .…”

“…코히어런스(coherence)는 결정행렬식에 대한 보다 실질 적인 측정치다. 위 행렬식 의 열방향 요소를 a 1 , a 2 ... , a n 이라고 했을 때, 의 코히어런스는 다음과 같이 나타낼 수 있다 [8], [14] .…”

A Survey on Compressive Sensing: Classical Results and Recent Advancements

“…This confirms the desire of using random matrices in compressive sensing. On the other hand, recent results are promising toward the practicality of deterministic matrices in terms of not only the compression ratio but also the complexity of the recovery process [3,23,58,83]. For example, deterministic sparse coding matrices have demonstrated to outperform both binary tree recovery and binary 1 -norm recovery methods in the so called binary compressive sensing, i.e., where x ∈ {0, 1} [80].…”

New Family of Polyphase Sequences with Low Correlation from Galois Rings

“…Pseudorandom sequences with low correlation have important applications in digital communications, radar ranging and cryptography [2], [3], [20]. For instance, a sequence set with sequences at least 2 can be used in the direct sequence spread spectrum (DSSS) system, in which each transmitter uses a unique sequence as its signature [4].…”