Variational methods have become an important kind of methods in signal and image restoration—a typical inverse problem. One important minimization model consists of the squared ?_2 data fidelity(corresponding to Gaus...Variational methods have become an important kind of methods in signal and image restoration—a typical inverse problem. One important minimization model consists of the squared ?_2 data fidelity(corresponding to Gaussian noise) and a regularization term constructed by a potential function composed of first order difference operators. It is well known that total variation(TV) regularization, although achieved great successes,suffers from a contrast reduction effect. Using a typical signal, we show that, actually all convex regularizers and most nonconvex regularizers have this effect. With this motivation, we present a general truncated regularization framework. The potential function is a truncation of existing nonsmooth potential functions and thus flat on(τ, +∞) for some positive τ. Some analysis in 1 D theoretically demonstrate the good contrast-preserving ability of the framework. We also give optimization algorithms with convergence verification in 2 D, where global minimizers of each subproblem(either convex or nonconvex) are calculated. Experiments numerically show the advantages of the framework.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11301289 and 11531013)
文摘Variational methods have become an important kind of methods in signal and image restoration—a typical inverse problem. One important minimization model consists of the squared ?_2 data fidelity(corresponding to Gaussian noise) and a regularization term constructed by a potential function composed of first order difference operators. It is well known that total variation(TV) regularization, although achieved great successes,suffers from a contrast reduction effect. Using a typical signal, we show that, actually all convex regularizers and most nonconvex regularizers have this effect. With this motivation, we present a general truncated regularization framework. The potential function is a truncation of existing nonsmooth potential functions and thus flat on(τ, +∞) for some positive τ. Some analysis in 1 D theoretically demonstrate the good contrast-preserving ability of the framework. We also give optimization algorithms with convergence verification in 2 D, where global minimizers of each subproblem(either convex or nonconvex) are calculated. Experiments numerically show the advantages of the framework.
