Adaptive regularized constrained least squares image restoration

Local Adaptive Image Filtering Based on Recursive Dilation Segmentation

This paper introduces a simple but effective image filtering method, namely, local adaptive image filtering (LAIF), based on an image segmentation method, i.e., recursive dilation segmentation (RDS). The algorithm is motivated by the observation that for the pixel to be smoothed, only the similar pixels nearby are utilized to obtain the filtering result. Relying on this observation, similar pixels are partitioned by RDS before applying a locally adaptive filter to smooth the image. More specifically, by directly taking the spatial information between adjacent pixels into consideration in a recursive dilation way, RDS is firstly proposed to partition the guided image into several regions, so that the pixels belonging to the same segmentation region share a similar property. Then, guided by the iterative segmented results, the input image can be easily filtered via a local adaptive filtering technique, which smooths each pixel by selectively averaging its local similar pixels. It is worth mentioning that RDS makes full use of multiple integrated information including pixel intensity, hue information, and especially spatial adjacent information, leading to more robust filtering results. In addition, the application of LAIF in the remote sensing field has achieved outstanding results, specifically in areas such as image dehazing, denoising, enhancement, and edge preservation, among others. Experimental results show that the proposed LAIF can be successfully applied to various filtering-based tasks with favorable performance against state-of-the-art methods.

A filtering approach to edge preserving MAP estimation of images

The authors present a computationally efficient technique for maximum a posteriori (MAP) estimation of images in the presence of both blur and noise. The image is divided into statistically independent regions. Each region is modelled with a WSS Gaussian prior. Classical Wiener filter theory is used to generate a set of convex sets in the solution space, with the solution to the MAP estimation problem lying at the intersection of these sets. The proposed algorithm uses an underlying segmentation of the image, and a means of determining the segmentation and refining it are described. The algorithm is suitable for a range of image restoration problems, as it provides a computationally efficient means to deal with the shortcomings of Wiener filtering without sacrificing the computational simplicity of the filtering approach. The algorithm is also of interest from a theoretical viewpoint as it provides a continuum of solutions between Wiener filtering and Inverse filtering depending upon the segmentation used. We do not attempt to show here that the proposed method is the best general approach to the image reconstruction problem. However, related work referenced herein shows excellent performance in the specific problem of demosaicing.

Nonlinear regularized reaction-diffusion filters for denoising of images with textures

Denoising is always a challenging problem in natural imaging and geophysical data processing. In this paper, we consider the denoising of texture images using a nonlinear reaction-diffusion equation and directional wavelet frames. In our model, a curvelet shrinkage is used for regularization of the diffusion process to preserve important features in the diffusion smoothing and a wave atom shrinkage is used as the reaction in order to preserve and enhance interesting oriented textures. We derive a digital reaction-diffusion filter that lives on graphs and show convergence of the corresponding iteration process. Experimental results and comparisons show very good performance of the proposed model for texture-preserving denoising.

Fast and stable bayesian image expansion using sparse edge priors

Smoothness assumptions in traditional image expansion cause blurring of edges and other high-frequency content that can be perceptually disturbing. Previous edge-preserving approaches are either ad hoc, statistically untenable, or computationally unattractive. We propose a new edge-driven stochastic prior image model and obtain the maximum a posteriori (MAP) estimate under this model. The MAP estimate is computationally challenging since it involves the inversion of very large matrices. An efficient algorithm is presented for expansion by dyadic factors. The technique exploits diagonalization of convolutional operators under the Fourier transform, and the sparsity of our edge prior, to speed up processing. Visual and quantitative comparison of our technique with other popular methods demonstrates its potential and promise.

Reconstruction of nonuniformly sampled images in spline spaces

This paper presents a novel approach to the reconstruction of images from nonuniformly spaced samples. This problem is often encountered in digital image processing applications. Nonrecursive video coding with motion compensation, spatiotemporal interpolation of video sequences, and generation of new views in multicamera systems are three possible applications. We propose a new reconstruction algorithm based on a spline model for images. We use regularization, since this is an ill-posed inverse problem. We minimize a cost function composed of two terms: one related to the approximation error and the other related to the smoothness of the modeling function. All the processing is carried out in the space of spline coefficients; this space is discrete, although the problem itself is of a continuous nature. The coefficients of regularization and approximation filters are computed exactly by using the explicit expressions of B-spline functions in the time domain. The regularization is carried out locally, while the computation of the regularization factor accounts for the structure of the nonuniform sampling grid. The linear system of equations obtained is solved iteratively. Our results show a very good performance in motion-compensated interpolation applications.