## JMI2013B-5 A generalization of the restricted isometry property and applications to compressed sensing (pp.129-133)

Author(s)： Hiroshi Inoue

J. Math-for-Ind. **5B** (2013) 129-133.

- File： JMI2013B-5.pdf (115KB)

Abstract

This paper introduces a new general theory of compressed sensing. We give a natural generalization of the restricted isometry property (RIP) called weak RIP. We consider the proposed theory to be more useful for real data analysis than the RIP. In this note, we verify the accuracy of the weak RIP by showing in reconstruction from undersampling measurements where it is possible to improve estimation in various situations.

Keyword(s). compressed sensing, restricted isometry constants, restricted isometry property, sparse approximation, sparse signal recovery, weak restricted isometry property