Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization

By José M. Bioucas-Dias, Mário A. T. Figueiredo. IEEE Transactions on Image Processing, 2009

362 citations recorded by the source corpus.

Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of difficulties with respect to the standard Gaussian additive noise scenario: (1) the noise is multiplied by (rather than added to) the original image; (2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of multiplicative noise models preclude the direct application of most state-of-the-art algorithms, which are designed for solving unconstrained optimization problems where the objective has two terms: a quadratic data term (log-likelihood), reflecting the additive and Gaussian nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a total variation or wavelet-based regularizer/prior). In this paper, we address these difficulties by: (1) converting the multiplicative model into an additive one by taking logarithms, as proposed by some other authors; (2) using variable splitting to obtain an equivalent constrained problem; and (3) dealing with this optimization problem using the augmented Lagrangian framework. A set of experiments shows that the proposed method, which we name MIDAL (multiplicative image denoising by augmented Lagrangian), yields state-of-the-art results both in terms of speed and denoising performance.

Subfields: Biomedical Engineering, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/a59a048481fbf80b4feba8b83ac2b6d0f295b786

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Citations in the corpus

SAR Image Despeckling Using a Convolutional Neural Network (2017, methodology): “Various methods have been developed in the literature to suppress speckle including multilook processing [3], [4], filtering methods [5]–[7], wavelet-based despecking methods [8]–[11], block-matching 3D (BM3D) algorithm [12] and total variation (TV) methods [13].”
NL-SAR: A Unified Nonlocal Framework for Resolution-Preserving (Pol)(In)SAR Denoising (2015, background): “achieves the best tradeoff between data fidelity and regularity, as defined in terms of wavelets coefficients distribution [7]–[12] or total variation of the image [13]–[16].”
Restoration of Poissonian Images Using Alternating Direction Optimization (2010, neutral): “Finally, the effectiveness of the resulting algorithm is illustrated in comparison with current state-of-the-art alternatives [11], [12], [19], [37], [39], via a set of experiments reported in Section VI.”
Hyperspectral image noise reduction based on rank-1 tensor decomposition (2013, background): “Bioucas-Dias and Figueiredo (2010) described a new approach to solve the optimization problem resulting from a variational estimation of images observed under multiplicative noise models.”
A Tutorial on Speckle Reduction in Synthetic Aperture Radar Images (2013, methodology): “Several solutions exist to apply TV methods in the case of multiplicative noise [118]–[124].”