Cishen Zhang

Zai Yang, Cishen Zhang, Jun Deng et al.

Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is presented to reformulate the basis pursuit problem for noiseless compressed sensing. Two algorithms are proposed based on convex optimization: one exactly solves the problem and the other is a relaxed version of the first one. The latter can be considered as a modified iterative soft thresholding algorithm and is easy to implement. Numerical simulation shows that, in dealing with noise-free measurements of sparse signals, the relaxed version is accurate, fast and competitive to the recent state-of-the-art algorithms. Its practical application is demonstrated in a more general case where signals of interest are approximately sparse and measurements are contaminated with noise.

Jiaxi He, Frank Z. Xing, Ran Yang et al.

The quality of images captured in outdoor environments can be affected by poor weather conditions such as fog, dust, and atmospheric scattering of other particles. This problem can bring extra challenges to high-level computer vision tasks like image segmentation and object detection. However, previous studies on image dehazing suffer from a huge computational workload and corruption of the original image, such as over-saturation and halos. In this paper, we present a novel image dehazing approach based on the optical model for haze images and regularized optimization. Specifically, we convert the non-convex, bilinear problem concerning the unknown haze-free image and light transmission distribution to a convex, linear optimization problem by estimating the atmosphere light constant. Our method is further accelerated by introducing a multilevel Haar wavelet transform. The optimization, instead, is applied to the low frequency sub-band decomposition of the original image. This dimension reduction significantly improves the processing speed of our method and exhibits the potential for real-time applications. Experimental results show that our approach outperforms state-of-the-art dehazing algorithms in terms of both image reconstruction quality and computational efficiency. For implementation details, source code can be publicly accessed via http://github.com/JiaxiHe/Image-and-Video-Dehazing.

Mehdi Korki, Jingxin Zhang, Cishen Zhang et al.

This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA) for reconstructing block-sparse signals with unknown block structures. Unlike the existing algorithms for block sparse signal recovery which assume the cluster structure of the nonzero elements of the unknown signal to be independent and identically distributed (i.i.d.), we use a more realistic Bernoulli-Gaussian hidden Markov model (BGHMM) to characterize the non-i.i.d. block-sparse signals commonly encountered in practice. The Block-IBA iteratively estimates the amplitudes and positions of the block-sparse signal using the steepest-ascent based Expectation-Maximization (EM), and optimally selects the nonzero elements of the block-sparse signal by adaptive thresholding. The global convergence of Block-IBA is analyzed and proved, and the effectiveness of Block-IBA is demonstrated by numerical experiments and simulations on synthetic and real-life data.

Zai Yang, Cishen Zhang, Lihua Xie

MR image sparsity/compressibility has been widely exploited for imaging acceleration with the development of compressed sensing. A sparsity-based approach to rigid-body motion correction is presented for the first time in this paper. A motion is sought after such that the compensated MR image is maximally sparse/compressible among the infinite candidates. Iterative algorithms are proposed that jointly estimate the motion and the image content. The proposed method has a lot of merits, such as no need of additional data and loose requirement for the sampling sequence. Promising results are presented to demonstrate its performance.