Abstract
ABSTRACT The performancelimitation of linear equalizers is studied forthe structural similarity (SSIM) criteria. Given a blurring fil-ter and an image with zero mean, the closed form formula isobtained to compute the maximal SSIM index and the corre-spondingoptimallinearequalizer. Theformulashowsthattheequalizer with maximal SSIM index is equal to the one withminimal mean square error (MSE) multiplied by a positivereal number. Numerical examples are given to demonstratethe theoretical results. Index Terms — Structure similarity; performance limita-tion; image restoration; linear equalizer 1. INTRODUCTION A quality-assessment measure, called structural similarity(SSIM) index, has been drawing much attention in the fieldof image/video processing [1]-[3], and has found a varietyof applications, ranging from image coding, restoration andfusion, to watermarkingand biometrics [3].The SSIM index represents the quality of a distorted im-agebycomparingthecorrelationsinluminance,contrast,andstructure, between the reference and distorted images [2]. Inmost existing works, SSIM has been used for quality evalu-ation and algorithm comparison purposes only. There havebeen efforts to use SSIM as optimization criteria in order toimprove perceived image/video quality in a number of im-age processing problems [3]-[8]. In particular, an algorithmwasproposedin[8]fordesigningtheoptimallinearfilter thatmaximizes the Stat-SSIM index,which is a statistical version
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