Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iterat...Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iteration into a continuous flow. The stability condition depends explicitly on smoothness of the image sequence, size of image domain, value of the regularization parameter, and finally discretization step. Specifically, as the discretization step approaches to zero, stability holds unconditionally. The analysis also clarifies relations among the iterative algorithm, the original variation formulation and the PDE system. The proper regularity of solution and natural images is briefly surveyed and discussed. Experimental results validate the theoretical claims both on convergence and exponential stability.展开更多
基金Supported by the National Natural Science Foundation of China(11661002,11601012)the College Scientific Research Fund of Ningxia(NGY2016136)+1 种基金the Key Project of North Minzu University(ZDZX201804)the First-class Disciplines Foundation of Ningxia(NXYLXK2017B09)
基金Foundation item： Projects（60835005, 90820302） supported by the National Natural Science Foundation of China Project（2007CB311001） supported by the National Basic Research Program of China
文摘Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iteration into a continuous flow. The stability condition depends explicitly on smoothness of the image sequence, size of image domain, value of the regularization parameter, and finally discretization step. Specifically, as the discretization step approaches to zero, stability holds unconditionally. The analysis also clarifies relations among the iterative algorithm, the original variation formulation and the PDE system. The proper regularity of solution and natural images is briefly surveyed and discussed. Experimental results validate the theoretical claims both on convergence and exponential stability.
