Multiplicative noise removal via a learned dictionary

Denoising of Fluorescence Image on the Surface of Quantum Dot/Nanoporous Silicon Biosensors

In the process of biological detection of porous silicon photonic crystals based on quantum dots, the concentration of target organisms can be indirectly measured via the change in the gray value of the fluorescence emitted from the quantum dots in the porous silicon pores before and after the biological reaction on the surface of the device. However, due to the disordered nanostructures in porous silicon and the roughness of the surface, the fluorescence images on the surface contain noise. This paper analyzes the type of noise and its influence on the gray value of fluorescent images. The change in the gray value caused by noise greatly reduces the detection sensitivity. To reduce the influence of noise on the gray value of quantum dot fluorescence images, this paper proposes a denoising method based on gray compression and nonlocal anisotropic diffusion filtering. We used the proposed method to denoise the quantum dot fluorescence image after DNA hybridization in a Bragg structure porous silicon device. The experimental results show that the sensitivity of digital image detection improved significantly after denoising.

Multiplicative Noise and Blur Removal by Framelet Decomposition and -Based L-Curve Method

This paper proposes a framelet-based convex optimization model for multiplicative noise and blur removal problem. The main idea is to employ framelet expansion to represent the original image and use the variable decomposition to solve the problem. Because of the nature of multiplicative noise, we decompose the observed data into the original image variable and the noise variable to obtain the resulting model. The original image variable is represented by framelet, and it is determined by using l₁-norm in the selection and shrinkage of framelet coefficients. The noise variable is measured by using the mean and the variance of the underlying probability distribution. This framelet setting can be applied to analysis, synthesis, and balanced approaches, and the resulting optimization models are convex, such that they can be solved very efficiently by the alternating direction of a multiplier method. An another contribution of this paper is to propose to select the regularization parameter by using the l₁-based L-curve method for these framelet based models. Numerical examples are presented to illustrate the effectiveness of these models and show that the performance of the proposed method is better than that by the existing methods.

A Nonlocal TV-Based Variational Method for PolSAR Data Speckle Reduction

In this paper, we propose a nonlocal total variation (NLTV)-based variational model for polarimetric synthetic aperture radar (PolSAR) data speckle reduction. This model, named WisNLTV, is obtained based on the Wishart fidelity term and the NLTV regularization defined for the complex-valued fourth-order tensor data. Since the proposed model is non-convex, an equivalent bi-convex model is obtained using the property of conjugate functions. Then, an efficient iteration algorithm is developed to solve the equivalent bi-convex model, based on the alternating minimization and the forward-backward operator splitting technique. The proposed iteration algorithm is proved to be convergent under certain conditions theoretically and numerically. Experimental results on both synthetic and real PolSAR data demonstrate that the proposed method can effectively reduce speckle noise and, meanwhile, better preserve the details and the repetitive structures such as textures and edges, and the polarimetric scattering characteristics, compared with the other methods.

Adaptive tight frame based multiplicative noise removal

Sparse approximation has shown to be a significant tool in improving image restoration quality, assuming that the targeted images can be approximately sparse under some transform operators. However, it is impossible for a fixed system to be always optimal for all the images. In this paper, we present an adaptive wavelet tight frame technology for sparse representation of an image with multiplicative noise. The adaptive wavelet tight frame is first learned from the logarithmic transformed given images, and then it is used to recover these images. Compared with the existing non-adaptive wavelet sparse transform methods, the numerical results demonstrate that the proposed adaptive tight frame scheme improves image restoration quality.

Speckle reduction via higher order total variation approach

Multiplicative noise (also known as speckle) reduction is a prerequisite for many image-processing tasks in coherent imaging systems, such as the synthetic aperture radar. One approach extensively used in this area is based on total variation (TV) regularization, which can recover significantly sharp edges of an image, but suffers from the staircase-like artifacts. In order to overcome the undesirable deficiency, we propose two novel models for removing multiplicative noise based on total generalized variation (TGV) penalty. The TGV regularization has been mathematically proven to be able to eliminate the staircasing artifacts by being aware of higher order smoothness. Furthermore, an efficient algorithm is developed for solving the TGV-based optimization problems. Numerical experiments demonstrate that our proposed methods achieve state-of-the-art results, both visually and quantitatively. In particular, when the image has some higher order smoothness, our methods outperform the TV-based algorithms.

Image noise reduction via geometric multiscale ridgelet support vector transform and dictionary learning

Advances in machine learning technology have made efficient image denoising possible. In this paper, we propose a new ridgelet support vector machine (RSVM) for image noise reduction. Multiscale ridgelet support vector filter (MRSVF) is first deduced from RSVM, to produce a multiscale, multidirection, undecimated, dyadic, aliasing, and shift-invariant geometric multiscale ridgelet support vector transform (GMRSVT). Then, multiscale dictionaries are learned from examples to reduce noises existed in GMRSVT coefficients. Compared with the available approaches, the proposed method has the following characteristics. The proposed MRSVF can extract the salient features associated with the linear singularities of images. Consequently, GMRSVT can well approximate edges, contours and textures in images, and avoid ringing effects suffered from sampling in the multiscale decomposition of images. Sparse coding is explored for noise reduction via the learned multiscale and overcomplete dictionaries. Some experiments are taken on natural images, and the results show the efficiency of the proposed method.

A dictionary learning approach for Poisson image deblurring

The restoration of images corrupted by blur and Poisson noise is a key issue in medical and biological image processing. While most existing methods are based on variational models, generally derived from a maximum a posteriori (MAP) formulation, recently sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, we propose in this paper a model containing three terms: a patch-based sparse representation prior over a learned dictionary, the pixel-based total variation regularization term and a data-fidelity term capturing the statistics of Poisson noise. The resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting. Extensive experimental results suggest that in terms of visual quality, peak signal-to-noise ratio value and the method noise, the proposed algorithm outperforms state-of-the-art methods.