Image deblurring, spectrum interpolation and application to satellite imaging

Durand, Sylvain; Malgouyres, François; Rougé, Bernard

doi:10.1051/cocv:2000117

Cited by 31 publications

(34 citation statements)

References 20 publications

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“…For convex energies (but not strictly convex, such as the model L 1 + T V ), we have obtained different minimizers for each of the three algorithms (sequential, divide-and-conquer, Ishikawa's algorithms), but with the same energy, as predicted by the theory. in [13,21,22]. We compare our results with the ones obtained by the duality-based algorithm of Chambolle which is presented in [9].…”

Section: Experiments and Discussionmentioning

confidence: 95%

Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization

2006

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Abstract. This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution of the discrete original problem. Furthermore we show that minimization of total variation under L 1 data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.

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Section: Experiments and Discussionmentioning

confidence: 95%

Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization

2006

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“…Finallly, a concrete application to satellite images is considered. While we had no access to images taken from satellites, the same procedure described and implemented in [8] was followed in order to simulate the typical degradation of satellite images, in order to appropriately compare degraded and restored images. First, the same convolution kernels were used as the ones described in [8] corresponding to two different satellites: SPOT 5 and a specific mode of SPOT 1.…”

Section: Psnr Time(s) Proposed Modelmentioning

confidence: 99%

“…These reference images are obtained by applying a prolate blur function to oversampled sharp images followed by down-sampling. The reader is referred to [8] for more details about the experiment. In this section, a comparison is offered between the proposed method and the simple ROF model for image restoration.…”

Section: Psnr Time(s) Proposed Modelmentioning

confidence: 99%

Image Restoration with a New Class of Forward-Backward-Forward Diffusion Equations of Perona--Malik Type with Applications to Satellite Image Enhancement

Guidotti¹,

Kim²,

Lambers³

2013

SIAM J. Imaging Sci.

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Abstract.A new class of anisotropic diffusion models is proposed for image processing which can be viewed either as a novel kind of regularization of the classical Perona-Malik model or, as advocated by the authors, as a new independent model. The models are diffusive in nature and are characterized by the presence of both forward and backward regimes. In contrast to the Perona-Malik model, in the proposed model the backward regime is confined to a bounded region, and gradients are only allowed to grow up to a large but tunable size, thus effectively preventing indiscriminate singularity formation, i.e., staircasing. Extensive numerical experiments demonstrate that the method is a viable denoising/deblurring tool. The method is significantly faster than competing state-of-the-art methods and appears to be particularly effective for simultaneous denoising and deblurring. An application to satellite image enhancement is also presented.

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“…Since we rely on noise estimates that have a certain accuracy, exceeding this accuracy in the data fitting is useless (as we will see later in this Section). Moreover, as it has been observed in all numerical experiments [14,16,17,18,19,20,24,29,10,31,44,49], using total variation as regularizer in denoising or restoration generally carries some loss of texture and it is not desirable to compute the solution that (absolutely) minimizes the TV but to keep a solution with a slightly higher TV value in order to avoid the loss of textures.…”

Section: Convergence Of the Fixed Point Algorithm For Simplicity Givenmentioning

confidence: 99%

“…Let us finally mention that many numerical algorithms have been proposed to minimize total variation (or similar models) subject to a global constraint as in (1.5) [44,29,14,49,17,18,19,20,24,16,45]. Imposing local constraints in a partition of the image was proposed in [43] and further developed in [13,5,4].…”

Section: Introductionmentioning

confidence: 99%

Irregular to Regular Sampling, Denoising, and Deconvolution

Facciolo¹,

Almansa²,

Aujol³

et al. 2009

Multiscale Model. Simul.

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Abstract. We propose a restoration algorithm for band limited images that considers irregular (perturbed) sampling, denoising, and deconvolution. We explore the application of a family of regularizers that allow to control the spectral behavior of the solution combined with the irregular to regular sampling algorithms proposed by H.G. Feichtinger, K. Gröchenig, M. Rauth and T. Strohmer. Moreover, the constraints given by the image acquisition model are incorporated as a set of local constraints. And the analysis of such constraints leads to an early stopping rule meant to improve the speed of the algorithm. Finally we present experiments focused on the restoration of satellite images, where the micro-vibrations are responsible of the type of distortions we are considering here. We will compare results of the proposed method with previous methods and show an extension to zoom.

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Image deblurring, spectrum interpolation and application to satellite imaging

Cited by 31 publications

References 20 publications

Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization

Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization

Image Restoration with a New Class of Forward-Backward-Forward Diffusion Equations of Perona--Malik Type with Applications to Satellite Image Enhancement

Irregular to Regular Sampling, Denoising, and Deconvolution

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