Shi Yunhui

Continuous wavelet transforms

In this paper, we propose a new type of continuous wavelet transform. However we discretize the variables of integral a and b, any numerical integral has a high resolution and a does not appear in the denominator of the integrand. Furthermore, we give two discretization methods of the new wavelet transform. For the one-dimensional situation, we give quadrature formula of the discretized inverse wavelet transform. For the multidimensional situation, we develop the commonly wavelet network based on the discretized inverse wavelet transform of the new wavelet transform. Finally, the numerical examples show that the continuous wavelet transform constructed in this paper has higher computing accuracy compared with the classical continuous wavelet transform.

Compressive sampling and sparse reconstruction of images/videos

Vision sensors usually do not account for the physical process of imaging and they acquire image/video samples at the Nyquist rate. The Nyquist rate is significantly higher than the effective dimensions of an image/video, and consequently compression is essential for the image/video prior to storage or transmission. The emerging Compressive Sensing (CS) theory states that a signal can be perfectly reconstructed, or can be robustly approximated in the presence of noise, using a few random measurements, provided that it is sparse in some linear transform domain. CS is the theoretical foundation for capturing a signal with effective information dimensions, and thus represents an unprecedented breakthrough in many fields such as sampling, processing, and recognition of image/video. We review the fundamental problems of CS for image/video including compressive sampling, sparse reconstruction models, and algorithms for the models. For compressive sampling, the construction of random and structural measurement matrices are considered separately and the performance of these two kinds of matrices is evaluated. For sparse reconstruction, models are classified as analysis-based or synthesisbased reconstruction models by the sparse representation prior, features of which are presented. The optimization models can be considered as constrained and unconstrained optimization problems. Some feasible algorithms for these two kinds of optimization problems are explained in detail and the performance of the algorithms is given. In addition, several challenges of compressive sensing technology are presented and future work is discussed.