Many inverse problems in applied mathematics can be formulated as the approximation of a target element $u$ in a complete metric space $(X,d_X)$ by the fixed point $\bar x$ of an appropriate contraction mapping $T : X \mapsto X$. The method of collage coding seeks to solve this problem by finding a contraction mapping $T$ that minimizes the so-called collage distance $d(x,Tx)$. In this paper, we develop a collage coding framework for inverse problems involving deterministic or random Hammerstein integral operators. Such operators are used to model image blurring. We illustrate the method with examples

Solving inverse problems for the Hammerstein integral equation and its random analog using the "collage method" for fixed points / H.E. Kunze, D. La Torre, K.M. Levere, E.R. Vrscay. - In: INTERNATIONAL JOURNAL OF PURE AND APPLIED MATHEMATICS. - ISSN 1311-8080. - 60:4(2010 Mar), pp. 393-408.

Solving inverse problems for the Hammerstein integral equation and its random analog using the "collage method" for fixed points

D. La Torre
Secondo
;
2010

Abstract

Many inverse problems in applied mathematics can be formulated as the approximation of a target element $u$ in a complete metric space $(X,d_X)$ by the fixed point $\bar x$ of an appropriate contraction mapping $T : X \mapsto X$. The method of collage coding seeks to solve this problem by finding a contraction mapping $T$ that minimizes the so-called collage distance $d(x,Tx)$. In this paper, we develop a collage coding framework for inverse problems involving deterministic or random Hammerstein integral operators. Such operators are used to model image blurring. We illustrate the method with examples
Collage theorem; Fixed point equations; Hammerstein integral equations; Inverse problems; Random fixed point equations
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/05 - Analisi Matematica
mar-2010
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/146337
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