A Bayesian Hyperprior Approach for Joint Image Denoising and Interpolation, with an Application to HDR Imaging

Recently, impressive denoising results have been achieved by Bayesian approaches which assume Gaussian models for the image patches. This improvement in performance can be attributed to the use of per-patch models. Unfortunately such an approach is particularly unstable for most inverse problems beyond denoising. In this work, we propose the use of a hyperprior to model image patches, in order to stabilize the estimation procedure. There are two main advantages to the proposed restoration scheme: Firstly it is adapted to diagonal degradation matrices, and in particular to missing data problems (e.g. inpainting of missing pixels or zooming). Secondly it can deal with signal dependent noise models, particularly suited to digital cameras. As such, the scheme is especially adapted to computational photography. In order to illustrate this point, we provide an application to high dynamic range imaging from a single image taken with a modified sensor, which shows the effectiveness of the proposed scheme.Comment: Some figures are reduced to comply with arxiv's size constraints. Full size images are available as HAL technical report hal-01107519v5, IEEE Transactions on Computational Imaging, 201

High Quality Image Interpolation via Local Autoregressive and Nonlocal 3-D Sparse Regularization

In this paper, we propose a novel image interpolation algorithm, which is formulated via combining both the local autoregressive (AR) model and the nonlocal adaptive 3-D sparse model as regularized constraints under the regularization framework. Estimating the high-resolution image by the local AR regularization is different from these conventional AR models, which weighted calculates the interpolation coefficients without considering the rough structural similarity between the low-resolution (LR) and high-resolution (HR) images. Then the nonlocal adaptive 3-D sparse model is formulated to regularize the interpolated HR image, which provides a way to modify these pixels with the problem of numerical stability caused by AR model. In addition, a new Split-Bregman based iterative algorithm is developed to solve the above optimization problem iteratively. Experiment results demonstrate that the proposed algorithm achieves significant performance improvements over the traditional algorithms in terms of both objective quality and visual perceptionComment: 4 pages, 5 figures, 2 tables, to be published at IEEE Visual Communications and Image Processing (VCIP) 201

Tension splines with application on image resampling

Digital raster images often need to be represented in higher and lower resolutions. Resampling of digital images is an essential part of image processing. Most efficient and sufficiently accurate image resampling techniques can produce spurious oscillations near sharp transitions of color. To improve that, we introduce tension splines applied dimension by dimension. The presented tension spline procedure provides an elegant solution to the image resampling by constructing a smooth approximation with sharp non-oscillatory resolution of discontinuities. The numerical results on real digital images are given to show effectiveness of the proposed algorithm

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio