Date of this Version
IEEE Transactions on Signal Processing
In this paper, we present a concise and coherent analysis of the constrained ??1 minimization method for stable recovering of high-dimensional sparse signals both in the noiseless case and noisy case. The analysis is surprisingly simple and elementary, while leads to strong results. In particular, it is shown that the sparse recovery problem can be solved via ??1 minimization under weaker conditions than what is known in the literature. A key technical tool is an elementary inequality, called Shifting Inequality, which, for a given nonnegative decreasing sequence, bounds the ??2 norm of a subsequence in terms of the ??1 norm of another subsequence by shifting the elements to the upper end.
minimisation, signal reconstruction, constrained minimization method, high-dimensional sparse signals, nonnegative decreasing sequence, shifting inequality, signal processing, sparse signals recovery, restricted isometry property, shifting inequality, sparse recovery
Cai, T., Wang, L., & Xu, G. (2010). Shifting Inequality and Recovery of Sparse Signals. IEEE Transactions on Signal Processing, 58 (3), 1300-1308. http://dx.doi.org/10.1109/TSP.2009.2034936
Date Posted: 27 November 2017
This document has been peer reviewed.