Open AccessPerturbation analysis of signal space fast iterative hard thresholding with redundant dictionaries
Author(s) -
Li Haifeng,
Liu Guoqi
Publication year - 2017
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2015.0366
Subject(s) - orthonormal basis , thresholding , oracle , computer science , algorithm , restricted isometry property , signal (programming language) , property (philosophy) , compressed sensing , convergence (economics) , mathematics , artificial intelligence , philosophy , physics , software engineering , epistemology , quantum mechanics , economics , image (mathematics) , programming language , economic growth
Practically, sparsity is expressed not in terms of an orthonormal basis but in terms an overcomplete dictionary. There are many practical examples in which a signal of interest is sparse in an overcomplete dictionary. The authors propose a new algorithm signal space fast iterative hard thresholding (SSFIHT) for the recovery of dictionary‐sparse signals. Under total perturbations, using D ‐restricted isometry property ( D ‐RIP), the authors provide the proof of convergence for SSFIHT. Comparing with the error of oracle recovery, it is easy to see that SSFIHT can provide oracle‐order recovery performance against total perturbations. Numerical simulations are performed to verify the conclusions.