Solve Mismatch Problem in Compressed Sensing

TL;DR

A novel algorithm is proposed to transform mismatch problem into matched by constructing a new measurement matrix to match measurement value under unknown measurement matrix and establish two types of algorithm, which are matched solution of unknown measurement matrix and calibration of unknown measurement matrix.

Abstract

This article proposes a novel algorithm for solving mismatch problem in compressed sensing. Its core is to transform mismatch problem into matched by constructing a new measurement matrix to match measurement value under unknown measurement matrix. Therefore, we propose mismatch equation and establish two types of algorithm based on it, which are matched solution of unknown measurement matrix and calibration of unknown measurement matrix. Experiments have shown that when under low gaussian noise levels, the constructed measurement matrix can transform the mismatch problem into matched and recover original images. The code is available: https://github.com/yanglebupt/mismatch-solution

Figures (12)

• Figure 1: Mismatch recovery results without noise. The first line is ground truth images, and the second line is the restored images
• Figure 2: Error curves of Algorithm.1. The horizontal axis is number of iteration and the vertical axis is error value. Same column shows the error curve of the same $PM_{image}$ in different iteration intervals.
• Figure 3: Error curves of Algorithm.2. The horizontal axis is number of iteration and the vertical axis is error value. Same column shows the error curve of the same $PM_{image}$ in different iteration intervals.
• Figure 4: Restored Baboon image using $A_{recv}$ constructed by Algorithm.1 and Algorithm.2 under three different $PM_{image}$. PM1 is GI image. PM2 is a image of lsun/tower dataset. PM3 is gray image of 0.5.
• Figure 5: Restored seven images using $A_{recv}$ constructed by Algorithm.1 (first line and it's error need multiple 1e-4) and Algorithm.2 (second line) under PM3.