An adaptive method for video denoising based on the ICI rule

This paper presents an adaptive video denoising technique based on the intersection of confidence intervals (ICI) rule used for adaptive filter support size calculation. The method is applied to three real-life video signals and its denoising performance is compared to a fixed size filter support based method resulting in a significant estimation error reduction in terms of the average frame peak signal-to-noise ratio (PSNR) improvement. The average frame PSNR obtained by using the here presented ICI based video denoising method is increased by up to 14.64 dB and by up to 23.74 dB when compared to the fixed size filter support based method. Furthermore, unlike the fixed size filter support based method, the adaptive ICI based method is shown to be efficient in a moving object edge preserving, while avoiding its blurring. The method performs well for both video signals obtained by recording stationary scenes, and video signals of moving objects, which are far more often encountered in practical applications, whereas the fixed size filter support based method is limited only to video signals of stationary scenes

Total Variation as a local filter

International audienceIn the Rudin-Osher-Fatemi (ROF) image denoising model, Total Variation (TV) is used as a global regularization term. However, as we observe, the local interactions induced by Total Variation do not propagate much at long distances in practice, so that the ROF model is not far from being a local filter. In this paper, we propose to build a purely local filter by considering the ROF model in a given neighborhood of each pixel. We show that appropriate weights are required to avoid aliasing-like effects, and we provide an explicit convergence criterion for an associated dual minimization algorithm based on Chambolle's work. We study theoretical properties of the obtained local filter, and show that this localization of the ROF model brings an interesting optimization of the bias-variance trade-off, and a strong reduction a ROF drawback called "staircasing effect". We finally present a new denoising algorithm, TV-means, that efficiently combines the idea of local TV-filtering with the non-local means patch-based method

Content-based image filtering

This paper presents an adaptive content-based image denoising technique. This technique uses image area classification for two purposes: perform more precise filtering and decrease computation complexity compared to modern filters of the same quality performance. Overview of several top image filtering techniques was made. Spatial domain (LPA-ICI), transform domain (SW-DCT) and combined filters (SA-DCT and BM3D) were studied in order to understand basic principles of image denoising. Image area classification which gives reasonable division into classes with clearly distinguishable properties for image filtering was observed. We have chosen block-wise classification that maps each block to Texture , Smooth and Edge classes. Performance of discussed filters on image area classes was shown. Adaptive free parameters choise for filtering quality improvement was analysed. It was shown that for some classes best parameters set differs from the best parameter set for the entire image. Methods to improve denoising algorithms speed which we were using in our adaptive solution were proposed. The most suitable algorithms with appropriate parameters set for each image area class were chosen. Modi ed classi cation algorithm applied to noisy images was developed. Whereupon, a modi ed BM3D-based adaptive denoising algorithm was proposed. Finally, multiple tests were performed and verification of speed and quality performances improvement compared to a baseline BM3D algorithm was obtained

Directional varying scale approximations for anisotropic signal processing

A spatially adaptive restoration of a multivariable anisotropic function given by uniformly sampled noisy data is considered. The presentation is given in terms of image processing as it allows a convenient and transparent motivation of basic ideas as well as a good illustration of results. To deal with the anisotropy discrete directional kernel estimates equipped with varying scale parameters are exploited. The local polynomial approximation (LPA) technique is modiÞed for a design of these kernels with a desirable polynomial smoothness. The nonlinearity of the method is incorporated by an intersection of conÞdence intervals (ICI) rule exploited in order to obtain adaptive varying scales of the kernel estimates for each direction. In this way we obtain the pointwise varying scale algorithm which is spatially adaptive to unknown smoothness and anisotropy of the function in question. Simulation experiments conÞrm the advanced performance of the new algorithms. 1

Models and Methods for Estimation and Filtering of Signal-Dependent Noise in Imaging

The work presented in this thesis focuses on Image Processing, that is the branch of Signal Processing that centers its interest on images, sequences of images, and videos. It has various applications: imaging for traditional cameras, medical imaging, e.g., X-ray and magnetic resonance imaging (MRI), infrared imaging (thermography), e.g., for security purposes, astronomical imaging for space exploration, three-dimensional (video+depth) signal processing, and many more.This thesis covers a small but relevant slice that is transversal to this vast pool of applications: noise estimation and denoising. To appreciate the relevance of this thesis it is essential to understand why noise is such an important part of Image Processing. Every acquisition device, and every measurement is subject to interferences that causes random fluctuations in the acquired signals. If not taken into consideration with a suitable mathematical approach, these fluctuations might invalidate any use of the acquired signal. Consider, for example, an MRI used to detect a possible condition; if not suitably processed and filtered, the image could lead to a wrong diagnosis. Therefore, before any acquired image is sent to an end-user (machine or human), it undergoes several processing steps. Noise estimation and denoising are usually parts of these fundamental steps.Some sources of noise can be removed by suitably modeling the acquisition process of the camera, and developing hardware based on that model. Other sources of noise are instead inevitable: high/low light conditions of the acquired scene, hardware imperfections, temperature of the device, etc. To remove noise from an image, the noise characteristics have to be first estimated. The branch of image processing that fulfills this role is called noise estimation. Then, it is possible to remove the noise artifacts from the acquired image. This process is referred to as denoising.For practical reasons, it is convenient to model noise as random variables. In this way, we assume that the noise fluctuations take values whose probabilities follow specific distributions characterized only by few parameters. These are the parameters that we estimate. We focus our attention on noise modeled by Gaussian distributions, Poisson distributions, or a combination of these. These distributions are adopted for modeling noise affecting images from digital cameras, microscopes, telescopes, radiography systems, thermal cameras, depth-sensing cameras, etc. The parameters that define a Gaussian distribution are its mean and its variance, while a Poisson distribution depends only on its mean, since its variance is equal to the mean (signal-dependent variance). Consequently, the parameters of a Poisson-Gaussian distribution describe the relation between the intensity of the noise-free signal and the variance of the noise affecting it. Degradation models of this kind are referred to as signal-dependent noise.Estimation of signal-dependent noise is commonly performed by processing, individually, groups of pixels with equal intensity in order to sample the aforementioned relation between signal mean and noise variance. Such sampling is often subject to outliers; we propose a robust estimation model where the noise parameters are estimated optimizing a likelihood function that models the local variance estimates from each group of pixels as mixtures of Gaussian and Cauchy distributions. The proposed model is general and applicable to a variety of signal-dependent noise models, including also possible clipping of the data. We also show that, under certain hypotheses, the relation between signal mean and noise variance can also be effectively sampled from groups of pixels of possibly different intensities.Then, we propose a spatially adaptive transform to improve the denoising performance of a specific class of filters, namely nonlocal transformdomain collaborative filters. In particular, the proposed transform exploits the spatial coordinates of nonlocal similar features from an image to better decorrelate the data, and consequently to improve the filtering. Unlike non-adaptive transforms, the proposed spatially adaptive transform is capable of representing spatially smooth coarse-scale variations in the similar features of the image. Further, based on the same paradigm, we propose a method that adaptively enhances the local image features depending on their orientation with respect to the relative coordinates of other similar features at other locations in the image.An established approach for removing Poisson noise utilizes so-called variance-stabilizing transformations (VST) to make the noise variance independent of the mean of the signal, hence enabling denoising by a standard denoiser for additive Gaussian noise. Within this framework, we propose an iterative method where at each iteration the previous estimate is summed back to the noisy image in order to improve the stabilizing performance of the transformation, and consequently to improve the denoising results. The proposed iterative procedure allows to circumvent the typical drawbacks that VSTs experience at very low intensities, and thus allows us to apply the standard denoiser effectively even at extremely low counts.The developed methods achieve state-of-the-art results in their respective field of application