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Register a new userAlternating minimization for a single step TV-Stokes model for image denoising
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Added by
Bin Wu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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The paper presents a fully coupled TV-Stokes model, and propose an algorithm based on alternating minimization of the objective functional whose first iteration is exactly the modified TV-Stokes model proposed earlier. The model is a generalization of the second order Total Generalized Variation model. A convergence analysis is given.
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We propose a set of iterative regularization algorithms for the TV-Stokes model to restore images from noisy images with Gaussian noise. These are some extensions of the iterative regularization algorithm proposed for the classical Rudin-Osher-Fatemi (ROF) model for image reconstruction, a single step model involving a scalar field smoothing, to the TV-Stokes model for image reconstruction, a two steps model involving a vector field smoothing in the first and a scalar field smoothing in the second. The iterative regularization algorithms proposed here are Richardsons iteration like. We have experimental results that show improvement over the original method in the quality of the restored image. Convergence analysis and numerical experiments are presented.
A complete multidimential TV-Stokes model is proposed based on smoothing a gradient field in the first step and reconstruction of the multidimensional image from the gradient field. It is the correct extension of the original two dimensional TV-Stokes to multidimensions. Numerical algorithm using the Chambolles semi-implicit dual formula is proposed. Numerical results applied to denoising 3D images and movies are presented. They show excellent performance in avoiding the staircase effect, and preserving fine structures.
We consider a low-rank tensor completion (LRTC) problem which aims to recover a tensor from incomplete observations. LRTC plays an important role in many applications such as signal processing, computer vision, machine learning, and neuroscience. A widely used approach is to combine the tensor completion data fitting term with a regularizer based on a convex relaxation of the multilinear ranks of the tensor. For the data fitting function, we model the tensor variable by using the Canonical Polyadic (CP) decomposition and for the low-rank promoting regularization function, we consider a graph Laplacian-based function which exploits correlations between the rows of the matrix unfoldings. For solving our LRTC model, we propose an efficient alternating minimization algorithm. Furthermore, based on the Kurdyka-{L}ojasiewicz property, we show that the sequence generated by the proposed algorithm globally converges to a critical point of the objective function. Besides, an alternating direction method of multipliers algorithm is also developed for the LRTC model. Extensive numerical experiments on synthetic and real data indicate that the proposed algorithms are effective and efficient.
Previous works have shown that convolutional neural networks can achieve good performance in image denoising tasks. However, limited by the local rigid convolutional operation, these methods lead to oversmoothing artifacts. A deeper network structure could alleviate these problems, but more computational overhead is needed. In this paper, we propose a novel spatial-adaptive denoising network (SADNet) for efficient single image blind noise removal. To adapt to changes in spatial textures and edges, we design a residual spatial-adaptive block. Deformable convolution is introduced to sample the spatially correlated features for weighting. An encoder-decoder structure with a context block is introduced to capture multiscale information. With noise removal from the coarse to fine, a high-quality noisefree image can be obtained. We apply our method to both synthetic and real noisy image datasets. The experimental results demonstrate that our method can surpass the state-of-the-art denoising methods both quantitatively and visually.
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating minimization algorithm. To speed up the algorithm, we also apply the continuation strategy to the penalty parameter. A convergence result is proved for the algorithm. Compared with the nonconvex ADMM, the proposed algorithm enjoys both theoretical and computational advantages like weaker convergence requirements and faster speed. Numerical results demonstrate the efficiency of the proposed algorithm.
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