Year: 2019
Type: article
Abstract: Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and it has become standard to replace it with an upper-bound. To ensure that this technique is suitable, [1] has introduced an upper-bound on the gap between the statistical dimension and its approximation. In this work, we first show that the error bound in [1] in some low-dimensional models such as total variation and ℓ1analysis minimization becomes poorly large. Next, we develop a new error bound which significantly improves the estimation gap compared to [1]. In particular, unlike the bound in [1] that fails in some settings with overcomplete dictionaries, our bound exhibits a decaying behavior in such cases.
Authors: Sajad Daei, Farzan Haddadi, Arash Amini, Martin Lotz
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2811112386