Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients

We address the denoising of images contaminated with multiplicative noise, e.g. speckle noise. Classical ways to solve such problems are filtering, statistical (Bayesian) methods, variational methods, and methods that convert the multiplicative noise into additive noise (using a logarithmic function), shrinkage of the coefficients of the log-image data in a wavelet basis or in a frame, and transform back the result using an exponential function. We propose a method composed of several stages: we use the log-image data and apply a reasonable under-optimal hard-thresholding on its curvelet transform; then we apply a variational method where we minimize a specialized criterion composed of an $\ell^1$ data-fitting to the thresholded coefficients and a Total Variation regularization (TV) term in the image domain; the restored image is an exponential of the obtained minimizer, weighted in a way that the mean of the original image is preserved. Our restored images combine the advantages of shrinkage and variational methods and avoid their main drawbacks. For the minimization stage, we propose a properly adapted fast minimization scheme based on Douglas-Rachford splitting. The existence of a minimizer of our specialized criterion being proven, we demonstrate the convergence of the minimization scheme. The obtained numerical results outperform the main alternative methods

Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization

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.Comment: 11 pages, 7 figures, 2 tables. To appear in the IEEE Transactions on Image Processing

DoPAMINE: Double-sided Masked CNN for Pixel Adaptive Multiplicative Noise Despeckling

We propose DoPAMINE, a new neural network based multiplicative noise despeckling algorithm. Our algorithm is inspired by Neural AIDE (N-AIDE), which is a recently proposed neural adaptive image denoiser. While the original N-AIDE was designed for the additive noise case, we show that the same framework, i.e., adaptively learning a network for pixel-wise affine denoisers by minimizing an unbiased estimate of MSE, can be applied to the multiplicative noise case as well. Moreover, we derive a double-sided masked CNN architecture which can control the variance of the activation values in each layer and converge fast to high denoising performance during supervised training. In the experimental results, we show our DoPAMINE possesses high adaptivity via fine-tuning the network parameters based on the given noisy image and achieves significantly better despeckling results compared to SAR-DRN, a state-of-the-art CNN-based algorithm.Comment: AAAI 2019 Camera Ready Versio