Solution of Linear Ill-Posed Problems Using Random Dictionaries

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

Sankhya B: The Indian Journal of Statistics, 2018, vol. 80, issue 1, No 9, 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
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DOI: 10.1007/s13571-018-0151-8

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