Variational model with nonstandard growth conditions for restoration of satellite optical images using synthetic aperture radar

D’Apice, Ciro; Manzo, Rosanna; Kogut, Peter I.

doi:10.1017/s0956792522000031

Cited by 5 publications

(5 citation statements)

References 34 publications

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“…So, the study of these issues for minimization problem (10) is the main subject of this section. (We can refer to [5,9,18,23] for some specific details that can appear in this case. )…”

Section: Existence Resultsmentioning

confidence: 99%

On a Variational Problem with a Nonstandard Growth Functional and Its Applications to Image Processing

et al. 2022

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We propose a new variational model in Sobolev–Orlicz spaces with non-standard growth conditions of the objective functional and discuss its applications to image processing. The characteristic feature of the proposed model is that the variable exponent, which is associated with non-standard growth, is unknown a priori and it depends on a particular function that belongs to the domain of objective functional. So, we deal with a constrained minimization problem that lives in variable Sobolev–Orlicz spaces. In view of this, we discuss the consistency of the proposed model, give the scheme for its regularization, derive the corresponding optimality system, and propose an iterative algorithm for practical implementations.

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“…So, the study of these issues for minimization problem (10) is the main subject of this section. (We can refer to [5,9,18,23] for some specific details that can appear in this case. )…”

Section: Existence Resultsmentioning

confidence: 99%

On a Variational Problem with a Nonstandard Growth Functional and Its Applications to Image Processing

et al. 2022

Self Cite

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“…Albeit PDEs with variable nonlinearity are rather interesting from the purely mathematical point of view as was mentioned before, their study is often motivated by various applications where the problem (1.2)-(1.4), or some special cases of it, appear in the most natural way [2,3,14,21]. It was recently shown that the model (1.2)-(1.4) naturally appears as the Euler-Lagrange equation in the problem of restoration of cloud contaminated satellite optical images [27]. Moreover, the above mentioned problem can be considered as a model for the deblurring and denoising of multi-spectral satellite images.…”

Section: Statement Of the Problemmentioning

confidence: 98%

Qualitative Analysis of an Optimal Sparse Control Problem for Quasi-Linear Parabolic Equation with Variable Order of Nonlinearity

D’Apice,

Kogut,

Manzo

2023

JODEA

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In this work, we study a sparse optimal control problem involving a quasilinear parabolic equation with variable order of nonlinearity as a state equation and with a pointwise control constraints. We show that in the case if the cost functional contains the terminal term of the tracking type, the proposed optimal control problem is ill-posed, in general. In view of this, we provide a sufficiently mild relaxation of the proposed problem and establish the existence of optimal solutions for the relaxed version. Using the compensated compactness technique and the consept of variational convergence of minimization problems, we study the attainability of optimal pairs to the relaxed problem by optimal solutions of the special approximating problems. We also discuss the optimality conditions for approximating problems and provide their substantiation.

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“…In what follows, with each function u ∈ W 1,1 ( ), we associate the so-called texture index p(|∇u|) using the rule (see Refs. [18][19][20] for comparison)…”

Section: Level Sets Directional Gradients and Texture Indexesmentioning

confidence: 99%

Variational Model with Nonstandard Growth Condition in Image Restoration and Contrast Enhancement

D’Apice,

Kogut,

Manzo

et al. 2024

Commun. Appl. Math. Comput.

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We propose a new variational model in Sobolev-Orlicz spaces with non-standard growth conditions of the objective functional and discuss its applications to the simultaneous contrast enhancement and denoising of color images. The characteristic feature of the proposed model is that we deal with a constrained non-convex minimization problem that lives in variable Sobolev-Orlicz spaces where the variable exponent is unknown a priori and it depends on a particular function that belongs to the domain of the objective functional. In contrast to the standard approach, we do not apply any spatial regularization to the image gradient. We discuss the consistency of the variational model, give the scheme for its regularization, derive the corresponding optimality system, and propose an iterative algorithm for practical implementations.

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Variational model with nonstandard growth conditions for restoration of satellite optical images using synthetic aperture radar

Cited by 5 publications

References 34 publications

On a Variational Problem with a Nonstandard Growth Functional and Its Applications to Image Processing

On a Variational Problem with a Nonstandard Growth Functional and Its Applications to Image Processing

Qualitative Analysis of an Optimal Sparse Control Problem for Quasi-Linear Parabolic Equation with Variable Order of Nonlinearity

Variational Model with Nonstandard Growth Condition in Image Restoration and Contrast Enhancement

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