A variational regularization model for multi-channel SAR image speckle reduction based on multiplicative-additive noise model

This paper presents a general methodology for nonparametric estimation of a function s related to a nonnegative real random variable X, under a constraint of type \(s(0)=c\). When a projection estimator of the target function is available, we explain how to modify it in order to obtain an estimator which satisfies the constraint. We extend risk bounds from the initial to the new estimator, and propose and study adaptive procedures for both estimators. The example of cumulative distribution function estimation illustrates the method for two different models: the multiplicative noise model (\(Y=XU\) is observed, with U following a uniform distribution) and the additive noise model \((Y=X+V\) is observed where V is a nonnegative nuisance variable with known density).

A new method for the automated extraction of pipelines and other linear objects from Synthetic Aperture Radar (SAR) scenes is presented. It combines intensity data with coherence data from an interferometric evaluation of a SAR scene pair. The fusion is based on Bayesian statistics and is part of a Markov random field (MRF) model for line extraction. Both intensity and coherence data are evaluated using rotating templates. The different statistical properties of intensity and coherence are taken into account by a multiplicative noise model and an additive noise model respectively. The MRF model introduces prior knowledge about the continuity and the narrowness of lines. Posterior odds resulting from the MRF method are input to a method based on ziplock snakes for linear object extraction. This processing step is controlled interactively which is necessary as fully automatic processing of the given noisy data does not provide sufficiently predictable results. The method is applied to data of the ERS tandem mission.

Addresses the problem of speech recognition with signals corrupted by additive noise at moderate signal-to-noise ratio (SNR). A model for additive noise is presented and used to compute the uncertainty about the hidden clean signal so as to weight the estimation provided by spectral subtraction. Weighted dynamic time warping (DTW) and Viterbi (HMM) algorithms are tested, and the results show that weighting the information along the signal can substantially increase the performance of spectral subtraction, an easily implemented technique, even with a poor estimation for noise and without using any information about the speaker. It is also shown that the weighting procedure can reduce the error rate when cepstral mean normalization is also used to cancel the convolutional noise.

Visible Light Communication (VLC) is a rising communication technology which uses Light-Emitting Diode (LED) luminaries for high-speed data transferring; however, the optical signal is usually degraded by the noise in the practical VLC system. In this paper, Allan Variance is introduced for noise analysis and modeling in VLC for the first time, which provides an efficient method to measure different kinds of noise in the VLC systems. By applying Allan variance to analyze the signals collected from the real-world environment, both white noise and random walk are observed in the VLC systems. The observed white noise and random walk are also modeled by using the Allan variance. The noise analysis and modeling based on Allan variance provide a method to improve the performance of VLC.

Speckles (multiplicative noise) in synthetic aperture radar (SAR) make it difficult to interpret the observed image. Due to the edge-preserving feature of total variation (TV), variational models with TV regularization have attracted much interest in reducing speckles. Algorithms based on the augmented Lagrangian function have been proposed to efficiently solve speckle-reduction variational models with TV regularization. However, these algorithms require inner iterations or inverses involving the Laplacian operator at each iteration. In this paper, we adapt Tseng's alternating minimization algorithm with a shifting technique to efficiently remove the speckle without any inner iterations or inverses involving the Laplacian operator. The proposed method is very simple and highly parallelizable; therefore, it is very efficient to despeckle huge-size SAR images. Numerical results show that our proposed method outperforms the state-of-the-art algorithms for speckle-reduction variational models with a TV regularizer in terms of central-processing-unit time.

A microarray-image model is used that takes into account many factors, including spot morphology, signal strength, background fluorescent noise, and shape and surface degradation. The model yields synthetic images whose appearance and quality reflect that of real microarray images. The model is used to link noise factors to the fidelity of signal extraction with respect to a standard image-extraction algorithm. Of particular interest is the identification of the noise factors and their interactions that significantly degrade the ability to accurately detect the true gene-expression signal. This study uses statistical criteria in conjunction with the simulation of various noise conditions to better understand the noise influence on signal extraction for cDNA microarray images. It proposes a paradigm that is implemented in software. It specifically considers certain kinds of noise in the noise model and sets these at certain levels; however, one can choose other types of noise or use different noise levels. In sum, it develops a statistical package that can work in conjunction with the existing image simulation toolbox.

Learning deep edge prior for image denoising

Restoration of speckle noise corrupted SAR images using regularization by denoising

Hyperspectral image (HSI) is often corrupted by various kinds of noises. This letter proposes an innovative HSI denoising approach by leveraging the graph signal processing (GSP) theory and the low-rank (LR) matrix recovery model. With GSP, the piecewise smoothness (PWS) property of the HSI can be efficiently characterized, leading to a new regularization for HSI denoising, termed the adaptive weight graph total variation (AWGTV) regularization. Then, the denoising problem is formulated into a constrained optimization problem that incorporates the AWGTV and the LR property of the HSI. An augmented Lagrange multiplier method is adopted to solve the problem. Numerical experiments conducted on synthetic and real-world datasets and comparisons with existing methods demonstrate the effectiveness of the proposed denoising algorithm.

In this paper, we consider the problem of nonlinear blind compressed sensing, i.e. jointly estimating the sparse codes and sparsity-promoting basis, under signal-dependent noise. We focus our efforts on the Poisson noise model, though other signal-dependent noise models can be considered. By employing a well-known variance stabilizing transform such as the Anscombe transform, we formulate our task as a nonlinear least squares problem with the l 1 penalty imposed for promoting sparsity. We solve this objective function under non-negativity constraints imposed on both the sparse codes and the basis. To this end, we propose a multiplicative update rule, similar to that used in non-negative matrix factorization (NMF), for our alternating minimization algorithm. To the best of our knowledge, this is the first attempt at a formulation for nonlinear blind compressed sensing, with and without the Poisson noise model. Further, we also provide some theoretical bounds on the performance of our algorithm.

This paper aims to provide realistic modelling of generic noise probability density functions (pdfs). The target is to obtain a parametric model depending on few parameters, and being so general to be able to describe many kinds of noise (e.g., symmetric or asymmetric, with variable sharpness). A very general and easy-to-use function which is based on HOS parameters is presented and compared with other HOS-based pdfs; it is called asymmetric generalized Gaussian. A real case study is considered for comparing the various pdfs; it consists in modelling real underwater acoustic noise at low frequencies and applying the estimated models to designed locally optimum detection (LOD) tests.

We consider quantum state transfer in a fully connected spin network, in which the results indicate that it is impossible to achieve high fidelity by free dynamics. However, the addition of certain kinds of noise can be helpful for this purpose. In fact, we introduce a model of Gaussian white noise affecting the spin-spin couplings (edges), except those linked to the input and output node, and prove that it enhances the fidelity of state transfer. The observed noise benefit is scale free as it applies to a quantum network of any size. The amount of the fidelity enhancement, depending on the noise strength as well as on the number of edges to which it is applied, can be so high as to take the fidelity close to one.

A recently investigated approach to noise filtering in digital images consists of considering a multiresolution decomposition of the input image, and applying a different adaptive filter to each resolution layer. The wavelet decomposition has been employed for multiresolution noise- reduction, thanks to its capability to capture spatial features within frequency subbands. Conversely, Laplacian pyramids (LP) look attractive because of their full band- pass frequency property, which enables connected image structures to be represented on multiple scales. The idea of the present work is to apply an adaptive minimum mean squared error filter to the connectivity-preserving different resolution layers into which the noisy image is decomposed. For natural images, each layer of the LP is characterized by a signal-to-noise ratio (SNR) that decreases for increasing spatial resolution. Therefore, each filter may be tuned to the SNR of the related layer, so as to preserve the spatial details of the less noisy layers to a larger extent. Once all the resolutions, including the base-band, have been adaptively smoothed, a noise-filtered image version is achieved by recombining the layers of the LP. Theoretical frameworks are developed for both additive and multiplicative noise models. Experimental results of de- noising carried out on images with simulated noise and on true synthetic aperture radar images validate the potentiality of the approach in terms of both SNR improvement and visual quality.

Variational models with second order regularizers can efficiently overcome the problems of staircasing effects caused by first order models. However, different types of second order regularizers may lead to different properties of feature preserving in restored images. In this paper, we show two variational models with second order regularizers. The first one is bounded Hessian model with Jacobian of normals, which uses bounded Jacobian of image intensity normals as regularizer, it is an extension of classical bounded Hessian (BH) model. The second one is total generalized variation model with Jacobian of normals, which is an extension to total generalized variation (TGV) model by replacing gradients in TGV with normals. The common objective is to improve feature preserving, such as edge, contrast and smoothness preservation. Additionally, their Alternating Direction Method of Multipliers (ADMM) are designed by introducing some proper auxiliary variables, Lagrange multipliers and penalty parameters to decompose the original models into some simple minimization sub-problems to solve. Extensive comparisons demonstrate that the proposed models are superior to the classical models with Hessian and TGV regularizers, especially in edge and corner preservation, smoothness, contrast enhancement. Moreover, the proposed models can be also extended to image inpainting, deblurring, and image enhancement.

In the last few years, Total Generalized Variation (TGV) regularization has proved to be a valuable tool to remove blur and noise from an image while avoiding the staircase effect typical of the Total Variation (TV) and preserving the sharp edges. The TGV-regularized model depends on two regularization parameters whose values must be appropriately selected to obtain good-quality restored images. In this work, we propose the use of the Balancing Principle (BP) to formulate the TGV-based image restoration problem as a constrained minimization problem whose objective is an implicit function of the two regularization parameters depending on the image to be restored. The values of the regularization parameters, and the corresponding restored image, satisfying the optimality condition of the formulated problem guarantee that the data fidelity and regularization terms are balanced. We introduce a Scaled Gradient Projection (SGP) method specifically tailored to the BP-based optimization problem and test its effectiveness against the fixed-point iteration schemes proposed in the literature. The numerical results performed on real-life images, affected by both Gaussian and Poisson noise, show that the proposed approach can effectively restore input images corrupted by several kinds of noise and outperform the fixed-point strategies for the realization of the Balancing Principle.