Pansharpening aims to fuse the geometry of a high-resolution panchromatic image with the color information of a low-resolution multispectral image to generate a high-resolution multispectral image. Classical variational methods are more interpretable and flexible than pure deep learning approaches, but their performance is limited by the use of rigid priors. In this paper, we efficiently combine both techniques by introducing a shallow residual network to learn the regularization term of a variational pansharpening model. The proposed energy includes the classical observation model for the multispectral data and a constraint to preserve the geometry encoded in the panchromatic. The experiments demonstrate that our method achieves state-of-the-art results.

We propose a new convex variational model for hyperspectral and multispectral image fusion. Our approach introduces nonlocal regularization conditioned to the geometry of the multispectral image and incorporates a constraint forcing the fusion product and the multispectral data to share modulated high frequencies. The proposed method is compared with state-of-the-art fusion techniques, showing competitive results for several quality metrics on different data.

The fusion of hyperspectral and multispectral images is a crucial task nowadays for it allows the extraction of relevant information from the fused image. Fusion consists of the combination of the spectral information of the hypespectral image (h) and the spatial information of the multispectral image (m). The fused image (f) has both good spatial and spectral information. In this paper we suggest a new hyperspectral and multispectral image (h-m) fusion approach based on Optimal Transport (OT) which highlights the idea of energy transfer from the starting images m and h to the resulting image f. The simulations show that the suggested method is effective and compares competitively with other state-of-the-art methods.

Common satellite imagery products consist of a panchromatic image at high spatial resolution and several misregistered spectral bands at lower resolution. Pansharpening is the fusion process by which a high-resolution multispectral image is inferred. We propose a variational model for which pan-sharpening is defined as an optimization problem minimizing a cost function with nonlocal regularization. We incorporate a new term preserving the radiometric ratio between the panchromatic and each spectral band. The resulting model is channel-decoupled, thus permitting the application to misregistered spectral data. The experimental results illustrate the superiority of the proposed method to preserve spatial details, reduce color artifacts, and avoid aliasing.

In this paper, we propose a new dual algorithm for the minimization of discrete nonconvex functionals, called half-linear regularization. Our approach alternates the calculation of a explicit weight with the minimization of a convex functional with respect to the solution. This minimization corresponds to the weighted total variation which is solved via the well-known Chambolle's algorithm. Finally, we present experimental results by applying it to some image restoration problems as denoising and deconvolution.

Pansharpening refers to the fusion process of inferring a high-resolution multispectral image from a high-resolution panchromatic image and a low-resolution multispectral one. In this paper we propose a new variational method for pansharpening which incorporates a nonlocal regularization term and two fidelity terms, one describing the relation between the panchromatic image and the high-resolution spectral channels and the other one preserving the colors from the low-resolution modality. The nonlocal term is based on the image self-similarity principle applied to the panchromatic image. The existence and uniqueness of minimizer for the described functional is proved in a suitable space of weighted integrable functions. Although quite successful in terms of relative error, state-of-the-art pansharpening methods introduce relevant color artifacts. These spectral distortions can be significantly reduced by involving the image self-similarity. Extensive comparisons with state-of-the-art algorithms are performed.

Demosaicking is the process by which from a matrix of colored pixels measuring only one color component per pixel, red, green, or blue, one can infer a whole color information at each pixel. This inference requires a deep understanding of the interaction between colors, and the involvement of image local geometry. Although quite successful in making such inferences with very small relative error, state-of-the-art demosaicking methods fail when the local geometry cannot be inferred from the neighboring pixels. In such a case, which occurs when thin structures or fine periodic patterns were present in the original, state-of-the-art methods can create disturbing artifacts, known as zipper effect, blur, and color spots. The aim of this paper is to show that these artifacts can be avoided by involving the image self-similarity to infer missing colors. Detailed experiments show that a satisfactory solution can be found, even for the most critical cases. Extensive comparisons with state-of-the-art algorithms will be performed on two different classic image databases.

Many classical image denoising methods are based on a local averaging of the color, which increases the signal/noise ratio. One of the most used algorithms is the neighborhood filter by Yaroslavsky or sigma filter by Lee, also called in a variant "SUSAN" by Smith and Brady or "Bilateral filter" by Tomasi and Manduchi. These filters replace the actual value of the color at a point by an average of all values of points which are simultaneously close in space and in color. Unfortunately, these filters show a "staircase effect," that is, the creation in the image of flat regions separated by artifact boundaries. In this paper, we first explain the staircase effect by finding the subjacent partial differntial equation (PDE) of the filter. We show that this ill-posed PDE is a variant of another famous image processing model, the Perona-Malik equation, which suffers the same artifacts. As we prove, a simple variant of the neighborhood filter solves the problem. We find the subjacent stable PDE of this variant. Finally, we apply the same correction to the recently introduced NL-means algorithm which had the same staircase effect, for the same reason.

State of the art movie restoration methods either estimate motion and filter out the trajectories, or compensate the motion by an optical flow estimate and then filter out the compensated movie. Now, the motion estimation problem is ill posed. This fact is known as the aperture problem: trajectories are ambiguous since they could coincide with any promenade in the space-time isophote surface. In this paper, we try to show that, for denoising, the aperture problem can be taken advantage of. Indeed, by the aperture problem, many pixels in the neighboring frames are similar to the current pixel one wishes to denoise. Thus, denoising by an averaging process can use many more pixels than just the ones on a single trajectory. This observation leads to use for movies a recently introduced image denoising method, the NL-means algorithm. This static 3D algorithm outperforms motion compensated algorithms, as it does not lose movie details. It involves the whole movie isophote and not just a trajectory.

We propose a new measure, the method noise, to evaluate and compare the performance of digital image denoising methods. We first compute and analyze this method noise for a wide class of denoising algorithms, namely the local smoothing filters. Second, we propose a new algorithm, the nonlocal means (NL-means), based on a nonlocal averaging of all pixels in the image. Finally, we present some experiments comparing the NL-means algorithm and the local smoothing filters.

In this work, we present and analyze an image denoising method, the NL-means algorithm, based on a non local averaging of all pixels in the image. We also introduce the concept of method noise, that is, the difference between the original (always slightly noisy) digital image and its denoised version. Finally, we present some experiences comparing the NL-means results with some classical denoising methods.

We address the problem of extending topographic maps to color images. A topographic map gives a morphological and a geometrical representation of the information contained in natural images. Two approaches are presented and discussed. The first one is new and consists in defining a total order in R/sup 3/ in accordance with the human visual percept ion of shapes. This allows one to define color topographic maps in the same way as for gray-level topographic maps. It has the advantage of leading all properties known in the gray-level case to remain true in the color case. However, the map contains a huge quantity of data that it has to be drastically simplified. The second approach allows one to build a simplified representation by using the geometry given by the luminance component only. We present experiments which illustrate the advantages and drawbacks of each of the method.

We discuss the physical generation process of images as a combination of basic operations: occlusions, transparencies and contrast changes. These operations generate the essential singularities which we call junctions. We deduce a mathematical and computational model for image analysis according to which the "atoms" of the image must be "pieces of level lines joining junctions", fitting the phenomenological description of Gaetano Kanizsa (1990). A parameter free junction detection algorithm is proposed for the computation of the previously defined "atoms". Then we propose an adequate modification of the morphological filtering algorithms so that they smooth the "atoms" without altering the junctions. Finally, we give some experiments on real and synthetic images.