Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

A multiresolution framework for local similarity based image denoising

In this paper, we present a generic framework for denoising of images corrupted with additive white Gaussian noise based on the idea of regional similarity. The proposed framework employs a similarity function using the distance between pixels in a multidimensional feature space, whereby multiple feature maps describing various local regional characteristics can be utilized, giving higher weight to pixels having similar regional characteristics. An extension of the proposed framework into a multiresolution setting using wavelets and scale space is presented. It is shown that the resulting multiresolution multilateral (MRM) filtering algorithm not only eliminates the coarse-grain noise but can also faithfully reconstruct anisotropic features, particularly in the presence of high levels of noise

A Tutorial on Speckle Reduction in Synthetic Aperture Radar Images

Speckle is a granular disturbance, usually modeled as a multiplicative noise, that affects synthetic aperture radar (SAR) images, as well as all coherent images. Over the last three decades, several methods have been proposed for the reduction of speckle, or despeckling, in SAR images. Goal of this paper is making a comprehensive review of despeckling methods since their birth, over thirty years ago, highlighting trends and changing approaches over years. The concept of fully developed speckle is explained. Drawbacks of homomorphic filtering are pointed out. Assets of multiresolution despeckling, as opposite to spatial-domain despeckling, are highlighted. Also advantages of undecimated, or stationary, wavelet transforms over decimated ones are discussed. Bayesian estimators and probability density function (pdf) models in both spatial and multiresolution domains are reviewed. Scale-space varying pdf models, as opposite to scale varying models, are promoted. Promising methods following non-Bayesian approaches, like nonlocal (NL) filtering and total variation (TV) regularization, are reviewed and compared to spatial- and wavelet-domain Bayesian filters. Both established and new trends for assessment of despeckling are presented. A few experiments on simulated data and real COSMO-SkyMed SAR images highlight, on one side the costperformance tradeoff of the different methods, on the other side the effectiveness of solutions purposely designed for SAR heterogeneity and not fully developed speckle. Eventually, upcoming methods based on new concepts of signal processing, like compressive sensing, are foreseen as a new generation of despeckling, after spatial-domain and multiresolution-domain method

Extended object reconstruction in adaptive-optics imaging: the multiresolution approach

We propose the application of multiresolution transforms, such as wavelets (WT) and curvelets (CT), to the reconstruction of images of extended objects that have been acquired with adaptive optics (AO) systems. Such multichannel approaches normally make use of probabilistic tools in order to distinguish significant structures from noise and reconstruction residuals. Furthermore, we aim to check the historical assumption that image-reconstruction algorithms using static PSFs are not suitable for AO imaging. We convolve an image of Saturn taken with the Hubble Space Telescope (HST) with AO PSFs from the 5-m Hale telescope at the Palomar Observatory and add both shot and readout noise. Subsequently, we apply different approaches to the blurred and noisy data in order to recover the original object. The approaches include multi-frame blind deconvolution (with the algorithm IDAC), myopic deconvolution with regularization (with MISTRAL) and wavelets- or curvelets-based static PSF deconvolution (AWMLE and ACMLE algorithms). We used the mean squared error (MSE) and the structural similarity index (SSIM) to compare the results. We discuss the strengths and weaknesses of the two metrics. We found that CT produces better results than WT, as measured in terms of MSE and SSIM. Multichannel deconvolution with a static PSF produces results which are generally better than the results obtained with the myopic/blind approaches (for the images we tested) thus showing that the ability of a method to suppress the noise and to track the underlying iterative process is just as critical as the capability of the myopic/blind approaches to update the PSF.Comment: In revision in Astronomy & Astrophysics. 19 pages, 13 figure

From uncertainty to adaptivity : multiscale edge detection and image segmentation

This thesis presents the research on two different tasks in computer vision: edge detection and image segmentation (including texture segmentation and motion field segmentation). The central issue of this thesis is the uncertainty of the joint space-frequency image analysis, which motivates the design of the adaptive multiscale/multiresolution schemes for edge detection and image segmentation. Edge detectors capture most of the local features in an image, including the object boundaries and the details of surface textures. Apart from these edge features, the region properties of surface textures and motion fields are also important for segmenting an image into disjoint regions. The major theoretical achievements of this thesis are twofold. First, a scale parameter for the local processing of an image (e.g. edge detection) is proposed. The corresponding edge behaviour in the scale space, referred to as Bounded Diffusion, is the basis of a multiscale edge detector where the scale is adjusted adaptively according to the local noise level. Second, an adaptive multiresolution clustering scheme is proposed for texture segmentation (referred to as Texture Focusing) and motion field segmentation. In this scheme, the central regions of homogeneous textures (motion fields) are analysed using coarse resolutions so as to achieve a better estimation of the textural content (optical flow), and the border region of a texture (motion field) is analysed using fine resolutions so as to achieve a better estimation of the boundary between textures (moving objects). Both of the above two achievements are the logical consequences of the uncertainty principle. Four algorithms, including a roof edge detector, a multiscale step edge detector, a texture segmentation scheme and a motion field segmentation scheme are proposed to address various aspects of edge detection and image segmentation. These algorithms have been implemented and extensively evaluated