Liang Xiao

Multiplicative noise removal via a novel variational model

Multiplicative noise appears in various image processing applications, such as synthetic aperture radar, ultrasound imaging, single particle emission-computed tomography, and positron emission tomography. Hence multiplicative noise removal is of momentous significance in coherent imaging systems and various image processing applications. This paper proposes a nonconvex Bayesian type variational model for multiplicative noise removal which includes the total variation (TV) and the Weberized TV as regularizer. We study the issues of existence and uniqueness of a minimizer for this variational model. Moreover, we develop a linearized gradient method to solve the associated Euler-Lagrange equation via a fixed-point iteration. Our experimental results show that the proposed model has good performance.

A weberized total variation regularization-based image multiplicative noise removal algorithm

Multiplicative noise removal is of momentous significance in coherent imaging systems and various image processing applications. This paper proposes a new nonconvex variational model for multiplicative noise removal under the Weberized total variation (TV) regularization framework. Then, we propose and investigate another surrogate strictly convex objective function for Weberized TV regularization-based multiplicative noise removal model. Finally, we propose and design a novel way of fast alternating optimizing algorithm which contains three subminimizing parts and each of them permits a closed-form solution. Our experimental results show that our algorithm is effective and efficient to filter out multiplicative noise while well preserving the feature details.

Compounded Regularization and Fast Algorithm for Compressive Sensing Deconvolution

Compressive Sensing Deconvolution (CS Deconvolution) is a new challenge problem encountered in a wide variety of image processing fields. A compound variational regularization model which combined total variation and curve let-based sparsity prior is proposed to recovery blurred image from compressive measurements. We propose a novel fast algorithm using variable-splitting and Dual Douglas-Rachford operator splitting methods. Experiments demonstrate our proposed algorithm can obtain high-resolution data from highly incomplete measurements.

Nonlocal total variation based speckle noise removal method for ultrasound image

Ultrasound images are widely used in diagnosis and therapy. However the existence of speckle will disgraces image quality and affects the tasks of individual interpretation and diagnosis. Nonlocal total variation (TV) denoising is one of the best denoising models and it is widely used to remove additive Gaussian noise. In this paper, we extend the application of nonlocal TV denoising model to remove speckle noise in ultrasound images. We present a model of the speckle noise in ultrasound images firstly. Then we propose an efficient algorithm to minimize the nonlocal TV energy based on the Split-Bregman method. At last we compare our nonlocal TV method with some well-known speckle noise filtering techniques and measure the denoising quality by different evaluating indicators. Experimental results show that the speckle noise can be efficiently removed by our method and the structure of the object can be well preserved, also our algorithm has the best performance among the algorithms of state-of-the-arts.

Variational image restoration based on Poisson singular integral and curvelet-type decomposition space regularization

Image restoration is a core topic of image processing. In this paper, we consider a variational restoration model consisting of Poisson singular integral (PSI) and curvelet-type decomposition space seminorm as regularizer. The PSI is used to impose a priori constraint on appropriate Lipschitz spaces, wherein a wide class of nonsmooth images can be accommodated. The seminorm of curvelet-type decomposition space is equivalent to the weighted curvelet coefficients which optimal represent smooth and edge parts of image with spar-sity. We propose efficient algorithm to solve the optimization problem based on the Douglas-Rachford splitting (DRS) technique. Experimental results demonstrate that our proposed method can preserve important image features, such as edges and textures.

Comments on Staircase effect alleviation by coupling gradient fidelity term

The paper staircase effect alleviation by coupling gradient fidelity term (Zhu Lixin and Xia Deshen, 2008 [1]) presented a nonlinear diffusion approach using a coupling gradient fidelity term. Although such approach helps to alleviate the staircase effect to some extent, the model is not sound. Moreover the physical mechanism of this model was explained incorrectly, and there are some theoretical mistakes in their proofs and propositions. We propose a new theoretical analysis of the alleviation staircase effect using a coupling gradient fidelity term.

A novel compound regularization and fast algorithm for compressive sensing deconvolution

Compressive Sensing Deconvolution (CS-Deconvolution) is a new challenge problem encountered in a wide variety of image processing fields. Since CS is more efficient for sparse signals, in our scheme, the input image is firstly sparse represented by curvelet frame system; then the curvelet coefficients are encoded by a structurally random matrix based CS sampling technique. In order to improve the CS-deconvolution performance, a compound variational regularization model, which combined total variation and curvelet-based sparsity prior, is proposed to recovery blurred image from compressive measurements. Given the compressive measurements, we propose a novel fast algorithm using variable-splitting and Dual Douglas-Rachford operator splitting methods to produce high quality deblurred results. Our method considerably improves the visual quality of CS reconstruction for the given number of random measurements and reduces the decoding computational complexity, compared to the existing CS-deconvolution methods.

A Nonlinear Inverse Scale Space Method for Multiplicative Noise Removal Based on Weberized Total Variation

Multiplicative noise removal has been drawn a greatly attention recently. Firstly, this paper proposes a new non-convex variational model for multiplicative noise removal under the Weberized TV regularization framework. Then we propose and study another surrogate strictly convex objective functional for Weberized TV regularization based multiplicative noise removal model. Finally, we adopt the recently proposed inverse scale space approach to estimate the underlying image under total variation (TV) regularization, in which a relaxation technique with two evolution equations is applied. Our experimental results show that the quality of images denoised is quite good and the detail information of restored images is well preserved by the proposed algorithm.

Perceptual Saliency Driven Total Variation for Image Denoising Using Tensor Voting

A nature image often contains various regions such as flat regions, ramps and edges with different singularities. A new perceptual saliency indicator is firstly proposed to distinguish edges and ramps. The proposed indicator is designed by a tensor voting approach with perceptual grouping performance. Using the perceptual saliency indicator, we propose a new variational model with an adaptive regularization term and a saliency weighted fidelity term. Experimental results demonstrate that our method has better performance in the staircase effect alleviation, the ramps and ridges preserving when compared with the state-of-the-art.

A Novel Image Compressive Sensing Approach with Column Sparse Prior

Compressive sensing is an international popular issue recently. In classical compressive sensing framework, the global sparse prior is employed to recovery image from the incomplete random projection, hence it is time consuming. In this paper we present a new image compressive sensing approach for image sparse recovery with column sparse prior. As opposed to compressive sensing, our model and algorithm based on 2D image matrices rather than 1D vectors so the image matrix does not need to be transformed into a vector prior to measurement and the size of sensing matrix can be greatly reduced. A new practical variant of GPSR algorithm is developed for the relevant optimization problems. To test our model and evaluate its performance, a series of experiments were performed in the paper. The experimental results indicated that our method can decrease the memory space cost and computational time on encoding and recovery.