Solution Of Linear Ill-Posed Problems Using Random Dictionaries

Keywords

Lasso; Linear inverse problem; Random dictionaries

Abstract

In the present paper, we consider an application of overcomplete dictionaries to the solution of general ill-posed linear inverse problems. In the context of regression problems, there has been an enormous amount of effort to recover an unknown function using such dictionaries. One of the most popular methods, lasso, and its versions, is based on minimizing the empirical likelihood and unfortunately, requires stringent assumptions on the dictionary, the so-called, compatibility conditions. Though compatibility conditions are hard to satisfy, it is well known that this can be accomplished by using random dictionaries. In the present paper, we show how one can apply random dictionaries to the solution of ill-posed linear inverse problems. We put a theoretical foundation under the suggested methodology and study its performance via simulations and real-data example.

Publication Date

1-1-2018

Publication Title

Sankhya: The Indian Journal of Statistics

Volume

80B

Number of Pages

178-193

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s13571-018-0151-8

Socpus ID

85050505848 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85050505848

This document is currently not available here.

Share

COinS