Economics at your fingertips  

Solution of Linear Ill-Posed Problems Using Random Dictionaries

Pawan Gupta and Marianna Pensky ()
Additional contact information
Pawan Gupta: University of Central Florida
Marianna Pensky: University of Central Florida

Sankhya B: The Indian Journal of Statistics, 2018, vol. 80, issue 1, 178-193

Abstract: 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.

Keywords: Linear inverse problem; Lasso; Random dictionaries; Primary 62G05; Secondary 62C10 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link) Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from

Access Statistics for this article

Sankhya B: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya B: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla ().

Page updated 2019-11-06
Handle: RePEc:spr:sankhb:v:80:y:2018:i:1:d:10.1007_s13571-018-0151-8