Xiaoqun Zhang

Some convex and nonconvex sparse reconstruction models and algorithms in imaging sciences


In this talk, I will present some sparse convex and nonconvex minimization models and algorithms that we developped for sparsity promoting in imaging sciences. We consider two applications such as Framelet based color image demoisacking with L1 based models, 3D bioluminscent tomography reconstruction under Poisson noise with L0 minimization. For the first part, I will present a two-stage regularization method based on sparse framelets representation of inter-color difference and individual channels in order to faithfully recover both geometry features and color consistency for color image restoration. The proposed models can be efficiently solved by Bregmanized operator splitting algorithm. Our numerical simulations show that our method presents start-ofthe-art results in terms of PSNR and visual quality. For the second part, we consider 3D Bioluminescence tomography (BLT) source reconstruction from Poisson data in three dimensional space. With a priori information of sources sparsity and MAP estimation of Poisson distribution, we study the minimization of Kullback-Leihbler divergence with l1 and l0 regularization. We show numerically that although several l1 minimization algorithms are efficient for compressive sensing, they fail for BLT reconstruction due to the high coherence of the measurement matrix columns and high nonlinearity of Poisson fitting term. Instead, we propose a novel greedy algorithm for l0 regularization to reconstruct sparse solutions for BLT problem. Numerical experiments on synthetic data obtained by the finite element methods and Monte-Carlo methods show the accuracy and efficiency of the proposed method.