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The restoration of images corrupted by blurring and structured noise has attracted growing attention in the domains of image processing and computer vision. However, many works only focus on the restoration of the images degraded by blurring and additive structured noise or multiplicative structured noise separately. It is still a challenge and an open problem to restore degraded images with blurring and multiplicative structured noise, simultaneously. In this paper, based on the total variation (TV), the statistical property of the Gamma noise and the maximum a posteriori (MAP) estimator, we obtain a convex variational model to recover blurred images with multiplicative structured noise. Especially, to get this convex model, we reformulate the prior assumption of the images degradation model by division instead of multiplication. For solving this convex model, an effective alternating direction method of multipliers (ADMM) is employed. Numerical experiments are presented to illustrate the effectiveness and efficiency of the proposed model.

Scene recovery is a fundamental imaging task for several practical applications, e.g., video surveillance and autonomous vehicles, etc. To improve visual quality under different weather/imaging conditions, we propose a real-time light correction method to recover the degraded scenes in the cases of sandstorms, underwater, and haze. The heart of our work is that we propose an intensity projection strategy to estimate the transmission. This strategy is motivated by a straightforward rank-one transmission prior. The complexity of transmission estimation is $O(N)$ where $N$ is the size of the single image. Then we can recover the scene in real-time. Comprehensive experiments on different types of weather/imaging conditions illustrate that our method outperforms competitively several state-of-the-art imaging methods in terms of efficiency and robustness., Comment: 9 pages, 6 figures, 1 table, Accepted by CVPR 2021

Image smoothing is a very important topic in image processing. Among these image smoothing methods, the L0 gradient minimization method is one of the most popular ones. However, the L0 gradient minimization method suffers from the staircasing effect and over-sharpening issue, which highly degrade the quality of the smoothed image. To overcome these issues, we use not only the L0 gradient term for finding edges, but also a surface area based term for the purpose of smoothing the inside of each region. An alternating minimization algorithm is suggested to efficiently solve the proposed model, where each subproblem has a closed-form solution. Leveraging the introduced surface area term, the proposed method can effectively alleviate the staircasing effect and the over-sharpening issue. The superiority of our method over the state-of-the-art methods is demonstrated by a series of experiments.

Single particle reconstruction (SPR) from cryo-electron microscopy (cryo-EM) is an emerging technique for determining the three-dimensional (3D) structure of macromolecules. A major challenge in single particle reconstruction from cryo-electron microscopy is to establish a reliable ab initio three-dimensional model using two-dimensional projection images. In this paper we introduce a fast proximal gradient method (FISTA) to solve the corresponding optimization problem of Single particle reconstruction. Numerical experiments with simulated images demonstrate that the proposed methods significantly reduce the estimation error and improved reconstruction quality.

As one of the most important image segmentation models, the Mumford-Shah functional was developed to pursue a piecewise smooth approximation of a given image based on the regularization on the total length of curves. In this paper, we modify the Mumford-Shah model using Euler's elastic a as the regularization. A two-stage segmentation method is applied the Euler's elastic a regularized Mumford-Shah model. The first stage is to find a smooth solution of the variant Mumford-Shah functional based on augmented Lagrangian method while a thresholding is performed in the second stage to obtain different phases for the segmentation. The K-means clustering method is used as the technique to find the thresholds for the segmentation. For intensity inhomogeneous images, we eliminate the effect of the bias field by bias-corrected fuzzy c-means method. Experimental results show that as the regularization, Euler's elastic a makes the Mumford-Shah model perform better for many kinds of images, including tubular and irregular shaped, CT Angiography (CTA) and MRI images in different noise level.

In this paper, we address the restoration of images corrupted by Poisson noise. The proposed new model contains two terms: one is from the sparse representation of the transformed image via variance stabilizing transformation (VST); the other is a data-fidelity term caused by the statistical properties of Poisson noise. The main algorithm is efficient. We first learn a dictionary to sparsely represent the transformed image using a state-of-the-art dictionary learning method, and then solve the minimization of the variational form by Newton method. Comparative experiments are carried out to show the leading performance of our new model.

This paper proposes a novel steganalyzer for detecting one of the most popular steganography, LSB matching (also known as “±1 embedding”). The histogram of difference image (the differences of adjacent pixels), which is usually a generalized Gaussian distribution centered at 0, is exploited for deriving statistical features. We have proved theoretically that the peak-value of the histogram would decrease after LSB matching embedding, while the renormalized histogram (the ratio of the histogram to the peak-value) would increase. Then we take the peak-value and the renormalized histogram as features for classification. Extensive experimental results show that the proposed steganalytic method outperforms some previous ones.

Matrix embedding is proved an effective way to improve embedding efficiency of steganography, and usually, higher dimensional matrix will provide better embedding efficiency. However, the sender might suffer huge computational complexity when employing high dimensional matrix. In this paper, a variation of matrix embedding is proposed. Instead of finding a coset leader as the modification of the cover image (which is the most time consuming step in matrix embedding), we turn to finding a vector in the coset which has relatively small Hamming weight. Such a vector can be found at reduced computational cost. Consequently, higher dimensional matrix can be used for practically implementable matrix embedding. The parity check matrix of random linear code is used in the experiments. It has shown that the proposed scheme can enhance the practicability and efficiency of the conventional matrix embedding.

As an important attribute directly influencing the steganographic scheme, the embedding efficiency is defined as the average number of random data bits per one embedding change. In this paper, we propose a novel approach to improve the embedding efficiency of LSB matching based on the sum and difference covering set (SDCS) of finite cyclic group. We show that the suitable choice of SDCS will lead to a new steganographic scheme which is more efficient than LSB matching. Then we illustrate that the new scheme keeps the statistical imperceptibility of LSB matching. The detailed constructions of SDCS are given and some related problems are also discussed.

In this paper, based on a careful investigation on the calibration (downsample) technique, we improve two detectors for detecting LSB matching: calibrated HCF COM and calibrated adjacency HCF COM. Instead of using the COM (center of mass) of the HCF (histogram characteristic function), we consider the ratio of the histogram's DFT coefficients of the image to the corresponding coefficients of the down-sampled image. Moreover, we propose to down-sample only for non-oscillating pixels. With a same level of computational complexity, the new detectors thus obtained are better than the old ones, especially for uncompressed images.

The goal of this paper is to report on experiments where we use Gabor dictionaries in a TV - linfin model for denoising. This allows many possible choices. Our conclusions are that the choice of the dictionary mostly impact the restoration of textures. Moreover, for most images, better results are obtained when the Gaussian term of the Gabor filters is close to isotropic