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Understanding Symmetric Smoothing Filters: A Gaussian Mixture Model Perspective

IEEE TRANSACTIONS ON IMAGE PROCESSING 2017年第11期26卷 5107-5121页

作者： Chan, Stanley H. Zickler, Todd Lu, Yue M. Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA Purdue Univ Dept Stat W Lafayette IN 47907 USA Harvard Univ John A Paulson Sch Engn & Appl Sci Cambridge MA 02138 USA

Many patch-based image denoising algorithms can be formulated as applying a smoothing filter to the noisy image. Expressed as matrices, the smoothing filters must be row normalized, so that each row sums to unity. Surprisingly, if we apply a column normalization before the row normalization, the performance of the smoothing filter can often be significantly improved. Prior works showed that such performance gain is related to the Sinkhorn-Knopp balancing algorithm, an iterative procedure that symmetrizes a row-stochastic matrix to a doubly stochastic matrix. However, a complete understanding of the performance gain phenomenon is still lacking. In this paper, we study the performance gain phenomenon from a statistical learning perspective. We show that Sinkhorn-Knopp is equivalent to an expectation-maximization (EM) algorithm of learning a Gaussian mixture model of the image patches. By establishing the correspondence between the steps of Sinkhorn-Knopp and the EM algorithm, we provide a geometrical interpretation of the symmetrization process. This observation allows us to develop a new denoising algorithm called Gaussian mixture model symmetric smoothing filter (GSF). GSF is an extension of the Sinkhorn-Knopp and is a generalization of the original smoothing filters. Despite its simple formulation, GSF outperforms many existing smoothing filters and has a similar performance compared with several state-of-the-art denoising algorithms.

关键词： Non-local means patch-based filtering patch prior expectation-maximization doubly-stochastic matrix symmetric smoothing filter

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Ultrasound Image Despeckling Using Stochastic Distance-based BM3D

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2017年第6期26卷 2632-2643页

作者： Santos, Cid A. N. Martins, Diego L. N. Mascarenhas, Nelson D. A. Univ Fed Sao Carlos Dept Comp BR-13565905 Sao Carlos Brazil Israelite Hosp Albert Einstein Dept Intervent Radiol BR-05651901 Sao Paulo Brazil Fac Campo Limpo Paulista BR-13231230 Campo Limpo Paulista Brazil

Ultrasound image despeckling is an important research field, since it can improve the interpretability of one of the main categories of medical imaging. Many techniques have been tried over the years for ultrasound despeckling, and more recently, a great deal of attention has been focused on patch-based methods, such as non-local means and block-matching collaborative filtering (BM3D). A common idea in these recent methods is the measure of distance between patches, originally proposed as the Euclidean distance, for filtering additive white Gaussian noise. In this paper, we derive new stochastic distances for the Fisher-Tippett distribution, based on well-known statistical divergences, and use them as patch distance measures in a modified version of the BM3D algorithm for despeckling log-compressed ultrasound images. State-of-the-art results in filtering simulated, synthetic, and real ultrasound images confirm the potential of the proposed approach.

关键词： Despeckling ultrasound imaging stochastic distances BM3D patch-based filtering

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Adaptive Image Denoising by Targeted Databases

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2015年第7期24卷 2167-2181页

作者： Luo, Enming Chan, Stanley H. Nguyen, Truong Q. Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA Purdue Univ Dept Stat W Lafayette IN 47907 USA

We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a database that contains relevant patches. We formulate the denoising problem as an optimal filter design problem and make two contributions. First, we determine the basis function of the denoising filter by solving a group sparsity minimization problem. The optimization formulation generalizes existing denoising algorithms and offers systematic analysis of the performance. Improvement methods are proposed to enhance the patch search process. Second, we determine the spectral coefficients of the denoising filter by considering a localized Bayesian prior. The localized prior leverages the similarity of the targeted database, alleviates the intensive Bayesian computation, and links the new method to the classical linear minimum mean squared error estimation. We demonstrate applications of the proposed method in a variety of scenarios, including text images, multiview images, and face images. Experimental results show the superiority of the new algorithm over existing methods.

关键词： patch-based filtering image denoising external database optimal filter non-local means BM3D group sparsity Bayesian estimation

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UNDERSTANDING SYMMETRIC SMOOTHING FILTERS VIA GAUSSIAN MIXTURES

UNDERSTANDING SYMMETRIC SMOOTHING FILTERS VIA GAUSSIAN MIXTU...

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IEEE International Conference on Image Processing (ICIP)

作者： Chan, Stanley H. Zickler, Todd Lu, Yue M. Purdue Univ Sch ECE W Lafayette IN 47907 USA Purdue Univ Dept Stat W Lafayette IN 47907 USA Harvard Univ Sch Engn & Appl Sci Cambridge MA 02138 USA

ISBN: (纸本)9781479983391

We study a class of smoothing filters for image denoising. Expressed as matrices, these smoothing filters must be row normalized so that each row sums to unity. Surprisingly, if one applies a column normalization to the matrix before the row normalization, the denoising quality can often be significantly improved. This column-row normalization corresponds to one iteration of a symmetrization process called the Sinkhorn-Knopp balancing algorithm. However, a complete understanding of the performance gain phenomenon is lacking. In this paper, we analyze the performance gain from a Gaussian mixture model (GMM) perspective. We show that the symmetrization is equivalent to an expectation-maximization (EM) algorithm for learning the GMM. Moreover, we make modifications to the symmetrization procedure and present a new denoising algorithm. Experimental results show that the new algorithm achieves comparable denoising results to some state-of-the-art methods.

关键词： Non-local means patch-based filtering Gaussian mixture model Expectation-Maximization doubly-stochastic matrix symmetric smoothing filter

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UNDERSTANDING SYMMETRIC SMOOTHING FILTERS VIA GAUSSIAN MIXTURES

UNDERSTANDING SYMMETRIC SMOOTHING FILTERS VIA GAUSSIAN MIXTU...

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IEEE International Conference on Image Processing

作者： Stanley H. Chan Todd Zickler Yue M. Lu School of ECE and Dept of Statistics Purdue University School of Engineering and Applied Sciences Harvard University

ISBN: (纸本)9781479983407

关键词： Non-local means patch-based filtering Gaussian mixture model Expectation-Maximization Doubly-stochastic matrix Symmetric smoothing filter smoothing filter Noise reduction smoothing Mixture models Gauss Filters CENTROSYMMETRIC Gm(m) Row of a Matrix normalization mixtures NONLOCAL POTENTIAL non-local interaction

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Monte Carlo Non-Local Means: Random Sampling for Large-Scale Image filtering

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2014年第8期23卷 3711-3725页

作者： Chan, Stanley H. Zickler, Todd Lu, Yue M. Harvard Univ Sch Engn & Appl Sci Cambridge MA 02138 USA

We propose a randomized version of the nonlocal means (NLM) algorithm for large-scale image filtering. The new algorithm, called Monte Carlo nonlocal means (MCNLM), speeds up the classical NLM by computing a small subset of image patch distances, which are randomly selected according to a designed sampling pattern. We make two contributions. First, we analyze the performance of the MCNLM algorithm and show that, for large images or large external image databases, the random outcomes of MCNLM are tightly concentrated around the deterministic full NLM result. In particular, our error probability bounds show that, at any given sampling ratio, the probability for MCNLM to have a large deviation from the original NLM solution decays exponentially as the size of the image or database grows. Second, we derive explicit formulas for optimal sampling patterns that minimize the error probability bound by exploiting partial knowledge of the pairwise similarity weights. Numerical experiments show that MCNLM is competitive with other state-of- the-art fast NLM algorithms for single-image denoising. When applied to denoising images using an external database containing ten billion patches, MCNLM returns a randomized solution that is within 0.2 dB of the full NLM solution while reducing the runtime by three orders of magnitude.

关键词： Non-local means Monte Carlo patch-based filtering sampling external denoising concentration of measure

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