Enhancing Compressed Sensing with Graph Structural Constraints: A Novel Approach to Active Learning in Measurement Matrices

Abstract

Compressed sensing on the graph, signals can be approximated by the graph and with the nodes containing information, so compressed sensing can collect information distributed on nodes or links. Also, compressed sensing on the graph becomes important due to the high cost of examining parameters one by one and the unavailability of information on some of them directly in the graph. In this article, by using the idea of ​​active learning and random walking, a method has been introduced to improve the construction of the measurement matrix in the field of the graph, so that information from the graph that is used in the construction of the measurement matrix (assuming that the measurement matrix is ​​underdetermined and non-horizontal) is introduced by the random walk method. They may be missed, identified, and, after observation, inserted into the measurement matrix, resulting in a stronger recovery of the original signal. To test this method, firstly, from the data set containing five hundred and ninety as the initial signal, the measurement matrix is ​​constructed with two random walking methods and the proposed method, and the output vector is obtained from it, then the initial thin signal is received with two recovery algorithms, convex optimization and model is recovered and finally calculates the amount of error and the degree of similarity of the four recovered signals compared to the original signal and from their comparison, it is clear that the recovery of the thin signal from the matrix made by the proposed method and the recovery with the convex optimization algorithm has the highest The degree of similarity and the lowest amount of error with the original signal is compared to the other three recovered signals.