The purpose of this paper is to investigate the ability of the infimal convolution regular- ization in curing the staircasing artifacts of the TV model in the SPECT reconstruction. We formulate the problem of SPECT re...The purpose of this paper is to investigate the ability of the infimal convolution regular- ization in curing the staircasing artifacts of the TV model in the SPECT reconstruction. We formulate the problem of SPECT reconstruction with the infimal convolution regu- larization as a convex three-block optimization problem and characterize its solution by a system of fixed-point equations in terms of the proximity operator of the functions involved in its objective function. We then develop a novel fixed-point proximity algorithm based on the fixed-point equations. Moreover, we introduce a preconditioning matrix motivated by the classical MLEM （maximum-likelihood expectation maximization） algorithm. We prove convergence of the proposed algorithm. The numerical results are included to show that the infimal convolution regularization is capable of effectively reducing the staircasing artifacts, while maintaining comparable image and coefficient recovery contrast. quality in terms of the signal-to-noise ratio展开更多
The authors give some sufficient conditions for the difference of two closed convex sets to be closed in general Banach spaces, not necessarily reflexive.
The author gives a new proof of Attouch Brezis′ theorem concerned with the duality for the sum of convex functions in general Banach spaces, and gives also some sufficient conditions for the difference of two close...The author gives a new proof of Attouch Brezis′ theorem concerned with the duality for the sum of convex functions in general Banach spaces, and gives also some sufficient conditions for the difference of two closed convex sets to be closed in reflexive Banach spaces.展开更多
文摘The purpose of this paper is to investigate the ability of the infimal convolution regular- ization in curing the staircasing artifacts of the TV model in the SPECT reconstruction. We formulate the problem of SPECT reconstruction with the infimal convolution regu- larization as a convex three-block optimization problem and characterize its solution by a system of fixed-point equations in terms of the proximity operator of the functions involved in its objective function. We then develop a novel fixed-point proximity algorithm based on the fixed-point equations. Moreover, we introduce a preconditioning matrix motivated by the classical MLEM （maximum-likelihood expectation maximization） algorithm. We prove convergence of the proposed algorithm. The numerical results are included to show that the infimal convolution regularization is capable of effectively reducing the staircasing artifacts, while maintaining comparable image and coefficient recovery contrast. quality in terms of the signal-to-noise ratio
文摘The authors give some sufficient conditions for the difference of two closed convex sets to be closed in general Banach spaces, not necessarily reflexive.
文摘The author gives a new proof of Attouch Brezis′ theorem concerned with the duality for the sum of convex functions in general Banach spaces, and gives also some sufficient conditions for the difference of two closed convex sets to be closed in reflexive Banach spaces.
