A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the non-local variations, jointly for the different components, through various $\ell_{1,p}$ matrix norms with $p \ge 1$. To facilitate the choice of the hyper-parameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for multispectral and hyperspectral images. The results demonstrate the interest of introducing a non-local structure tensor regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods

A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution

To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order derivative based total $\alpha$-order variation model, which can outperform the currently popular high order regularization models. There exist several previous works using total $\alpha$-order variations for image restoration; however first no analysis is done yet and second all tested formulations, differing from each other, utilize the zero Dirichlet boundary conditions which are not realistic (while non-zero boundary conditions violate definitions of fractional-order derivatives). This paper first reviews some results of fractional-order derivatives and then analyzes the theoretical properties of the proposed total $\alpha$-order variational model rigorously. It then develops four algorithms for solving the variational problem, one based on the variational Split-Bregman idea and three based on direct solution of the discretise-optimization problem. Numerical experiments show that, in terms of restoration quality and solution efficiency, the proposed model can produce highly competitive results, for smooth images, to two established high order models: the mean curvature and the total generalized variation.Comment: 26 page

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

Universal Denoising Networks : A Novel CNN Architecture for Image Denoising

We design a novel network architecture for learning discriminative image models that are employed to efficiently tackle the problem of grayscale and color image denoising. Based on the proposed architecture, we introduce two different variants. The first network involves convolutional layers as a core component, while the second one relies instead on non-local filtering layers and thus it is able to exploit the inherent non-local self-similarity property of natural images. As opposed to most of the existing deep network approaches, which require the training of a specific model for each considered noise level, the proposed models are able to handle a wide range of noise levels using a single set of learned parameters, while they are very robust when the noise degrading the latent image does not match the statistics of the noise used during training. The latter argument is supported by results that we report on publicly available images corrupted by unknown noise and which we compare against solutions obtained by competing methods. At the same time the introduced networks achieve excellent results under additive white Gaussian noise (AWGN), which are comparable to those of the current state-of-the-art network, while they depend on a more shallow architecture with the number of trained parameters being one order of magnitude smaller. These properties make the proposed networks ideal candidates to serve as sub-solvers on restoration methods that deal with general inverse imaging problems such as deblurring, demosaicking, superresolution, etc.Comment: Camera ready paper to appear in the Proceedings of CVPR 201

QuaSI: Quantile Sparse Image Prior for Spatio-Temporal Denoising of Retinal OCT Data

Optical coherence tomography (OCT) enables high-resolution and non-invasive 3D imaging of the human retina but is inherently impaired by speckle noise. This paper introduces a spatio-temporal denoising algorithm for OCT data on a B-scan level using a novel quantile sparse image (QuaSI) prior. To remove speckle noise while preserving image structures of diagnostic relevance, we implement our QuaSI prior via median filter regularization coupled with a Huber data fidelity model in a variational approach. For efficient energy minimization, we develop an alternating direction method of multipliers (ADMM) scheme using a linearization of median filtering. Our spatio-temporal method can handle both, denoising of single B-scans and temporally consecutive B-scans, to gain volumetric OCT data with enhanced signal-to-noise ratio. Our algorithm based on 4 B-scans only achieved comparable performance to averaging 13 B-scans and outperformed other current denoising methods.Comment: submitted to MICCAI'1

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