This diploma thesis deals with the problem of using an objective quality assessment methods in image data compression. Lossy compression always introduces some kind of distortion into the processed data causing degradation in the quality of the image. The intensity of this distortion can be measured using subjective or objective methods. To be able to optimize compression algorithms the objective criteria are used. In this work the SSIM index as a useful tool for describing the quality of compressed images has been presented. Lossy compression scheme is realized using the wavelet transform and SPIHT algorithm. The modification of this algorithm using partitioning of the wavelet coefficients into the separate tree-preserving blocks followed by independent coding, which is especially suitable for parallel processing, was implemented. For the given compression ratio the traditional problem is being solved – how to allocate available bits among the spatial blocks to achieve the highest possible image quality. The possible approaches to achieve this solution were discussed. As a result, some methods for bit allocation based on MSSIM index were proposed. To test the effectivity of these methods the MATLAB environment was used.

Dans cette thèse CIFRE en collaboration entre le Centre de Mathématiques et de leurs Applications, École Normale Supérieure de Cachan et l’entreprise DxO, nous abordons le problème de la décomposition additive d’une image en base et détail. Une telle décomposition est un outil fondamental du traitement d’image. Pour une application à la photographie professionnelle dans le logiciel DxO Photolab, il est nécessaire que la décomposition soit exempt d’artefact. Par exemple, dans le contexte de l’amélioration de contraste, où la base est réduite et le détail augmenté, le moindre artefact devient fortement visible. Les distorsions de l’image ainsi introduites sont inacceptables du point de vue d’un photographe.L’objectif de cette thèse est de trouver et d’étudier les filtres les plus adaptés pour effectuer cette tâche, d’améliorer les meilleurs et d’en définir de nouveaux. Cela demande une mesure rigoureuse de la qualité de la décomposition en base plus détail. Nous examinons deux artefact classiques (halo et staircasing) et en découvrons trois autres types tout autant cruciaux : les halos de contraste, le cloisonnement et les halos sombres. Cela nous conduit à construire cinq mire adaptées pour mesurer ces artefacts. Nous finissons par classer les filtres optimaux selon ces mesures, et arrivons à une décision claire sur les meilleurs filtres. Deux filtres sortent du rang, dont un proposé dans cette thèse. / In this CIFRE thesis, a collaboration between the Center of Mathematics and their Applications, École Normale Supérieure de Cachan and the company DxO, we tackle the problem of the additive decomposition of an image into base and detail. Such a decomposition is a fundamental tool in image processing. For applications to professional photo editing in DxO Photolab, a core requirement is the absence of artifacts. For instance, in the context of contrast enhancement, in which the base is reduced and the detail increased, minor artifacts becomes highly visible. The distortions thus introduced are unacceptable from the point of view of a photographer.The objective of this thesis is to single out and study the most suitable filters to perform this task, to improve the best ones and to define new ones. This requires a rigorous measure of the quality of the base plus detail decomposition. We examine two classic artifacts (halo and staircasing) and discover three more sorts that are equally crucial: contrast halo, compartmentalization, and the dark halo. This leads us to construct five adapted patterns to measure these artifacts. We end up ranking the optimal filters based on these measurements, and arrive at a clear decision about the best filters. Two filters stand out, including one we propose.