We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point ¯f is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.

IFSM fractal image compression with entropy and sparsity constraints: A sequential quadratic programming approach / H. Kunze, D. La Torre, J. Lin (AIP CONFERENCE PROCEEDINGS). - In: ICNPAA 2016 : World Congress[s.l] : American Institute of Physics, 2017 Feb. - ISBN 9780735414648. - pp. 020090-1-020090-7 (( Intervento presentato al 11. convegno ICNPAA tenutosi a La Rochelle nel 2016 [10.1063/1.4972682].

IFSM fractal image compression with entropy and sparsity constraints: A sequential quadratic programming approach

D. La Torre
Secondo
;
J. Lin
2017-02

Abstract

We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point ¯f is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/482641
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