journal homepage: www.elsevier.com/locate/media Detection of neuron membranes in electron microscopy images using a serial

Abstract Non-local methods for image denoising and inpainting have gained considerable attention in recent years. This is in part due to their superior performance in textured images, a known weakness of purely local methods. Local methods on the other hand have demonstrated to be very appropriate for the recovering of geometric structures such as image edges. The synthesis of both types of methods is a trend in current research. Variational analysis in particular is an appropriate tool for a unified treatment of local and non-local methods. In this work we propose a general variational framework non-local image inpainting, from which important and representative previous inpainting schemes can be derived, in addition to leading to novel ones. We explicitly study some of these, relating them to previous work and showing results on synthetic and real images.

Abstract—The present paper contributes two novel techniques in the context of image restoration by nonlocal filtering. Firstly, we introduce an efficient implementation of the nonlocal means filter based on arranging the data in a cluster tree. The structuring of data allows for a fast and accurate preselection of similar patches. In contrast to previous approaches, the preselection is based on the same distance measure as used by the filter itself. It allows for large speedups, especially when the search for similar patches covers the whole image domain, i.e., when the filter is truly nonlocal. However, also in the windowed version of the filter, the cluster tree approach compares favorably to previous techniques in respect of quality versus computational cost. Secondly, we suggest an iterative version of the filter that is derived from a variational principle and is designed to yield non-trivial steady states. It reveals to be particularly useful in

Recent developments in computational imaging and restoration have heralded the arrival and convergence of several powerful methods for adaptive processing of multidimensional data. Examples include Moving Least Square (from Graphics), the Bilateral Filter and Anisotropic Diffusion (from Machine Vision), Boosting and Spectral Methods (from Machine Learning), Non-local Means (from Signal Processing), Bregman Iterations (from Applied Math), Kernel Regression and Iterative Scaling (from Statistics). While these approaches found their inspirations in diverse fields of nascence, they are deeply connected. In this paper I present a practical and unified framework to understand some of the basic underpinnings of these methods, with the intention of leading the reader to a broad understanding of how they interrelate. I also illustrate connections between these techniques and Bayesian approaches. The proposed framework is used to arrive at new insights, methods, and both practical and theoretical results. In particular, several novel optimality properties of algorithms in wide use such as BM3D, and methods for their iterative improvement (or non-existence thereof) are discussed. Several theoretical results are discussed which will enable the performance analysis and subsequent improvement of any existing restoration algorithm. While much of the material discussed is applicable to wider class of linear degradation models (e.g. noise, blur, etc.,) in order to keep matters focused, we consider the problem of denoising here.

Recent developments in computational imaging and restoration have heralded the arrival and convergence of several powerful methods for adaptive processing of multidimensional data. Examples

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In this paper, we propose a denoising method motivated by our previous analysis [1], [2] of the performance bounds for image denoising. Insights from that study are used here to derive a highperformance, practical denoising algorithm. We propose a patch-based Wiener filter that exploits patch redundancy for image denoising. Our framework uses both geometrically as well as photometrically similar patches to estimate the different filter parameters. We describe how these parameters can be accurately estimated directly from the input noisy image. Our denoising approach, designed for nearoptimal performance (in the mean squared error sense), has a sound statistical foundation that is analyzed in detail. The performance of our approach is verified experimentally on a variety of images and noise levels. The results presented here demonstrate that our proposed method is on par or exceeding the current state-of-the-art, both visually and quantitatively.

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Abstract—In this paper, we propose a denoising method motivated by our previous analysis of the performance bounds for image denoising. Insights from that study are used here to derive a high-performance practical denoising algorithm. We propose a patch-based Wiener filter that exploits patch redundancy for image denoising. Our framework uses both geometrically and photometrically similar patches to estimate the different filter parameters. We describe how these parameters can be accurately estimated directly from the input noisy image. Our denoising approach, designed for near-optimal performance (in the mean-squared error sense), has a sound statistical foundation that is analyzed in detail. The performance of our approach is experimentally verified on a variety of images and noise levels. The results presented here demonstrate that our proposed method is on par or exceeding the current state of the art, both visually and quantitatively. Index Terms—Denoising bounds, image clustering, image denoising, linear minimum mean-squared-error (LMMSE) estimator, Wiener filter.

We propose in this paper to unify two different approachestoimagerestoration:Ontheonehand,learninga basisset(dictionary)adaptedtosparsesignaldescriptions hasproventobeveryeffectiveinimagereconstructionand classificationtasks.Ontheotherhand,explicitlyexploiting theself-similaritiesofnaturalimageshasledtothesuccessfulnon-localmeansapproachtoimagerestoration.Weproposesimultaneoussparsecodingasaframeworkforcombiningthesetwoapproachesinanaturalmanner. Thisis achievedbyjointlydecomposinggroupsofsimilarsignals onsubsetsofthelearneddictionary. Experimentalresults inimagedenoisinganddemosaickingtaskswithsynthetic andrealnoiseshowthattheproposedmethodoutperforms thestateoftheart,makingitpossibletoeffectivelyrestore rawimagesfromdigitalcamerasatareasonablespeedand