Convex Approximation Technique for Interacting Line Elements Deblurring: a New Approach

  • Authors:

  • Antonio Boccuto;Ivan Gerace;Patrizia Pucci

  • Affiliations:

  • Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy 06123;Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy 06123;Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy 06123

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2012

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Abstract

The problem of image restoration from blur and noise is studied. A solution of the problem is understood as the minimum of an energy function composed by two terms. The first is the data fidelity term, while the latter is related to the smoothness constraints. The discontinuities of the ideal image are unknown and must be estimated. In particular, the involved images are supposed to be piecewise continuous and with thin and continuous edges. In this paper we assume that the smoothness constraints can be either of the first order, or the second order, or the third order. The energy function that implicitly refers to discontinuities is called dual energy function. To minimize the non-convex dual energy, a GNC (Graduated Non-Convexity) technique is used. The GNC algorithm proposed in this paper is indicated as CATILED, short for Convex Approximation Technique for Interacting Line Elements Deblurring. We also prove in the Appendix the new duality Theorem 3 stated in Sect. 3. Theorem 3 shows that the first convex approximation defined in CATILED has good qualities for the reconstruction. The experimental results, given in Sect. 10, confirm the applicability of the technique.