Image definition measurement plays an important role in various image processing applications.And a reliable objective image definition metrics is critical for evaluating the definition of the restored image.In this p...Image definition measurement plays an important role in various image processing applications.And a reliable objective image definition metrics is critical for evaluating the definition of the restored image.In this paper,a novel image distortion metric based on minimal Total Bounded Variation(TBV) is presented.It is clarified that when the restored image approximates to the original clear image,the smaller the TBV is,the better the definition of the restored image is.Furthermore,the difference between the restored image and the original clear image is the smallest when the TBV is minimum.In numerical results,the TBV of the original clear image,blur image and restored image are presented and compared,and the results demonstrate the validity of the distortion metric proposed.展开更多
We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）...We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）×l^1（Z^d）×…×l^1（Z^d）to BV（Z^d）,where BV（Z^d）is the set of functions of bounded variation defined on Zd.Moreover,two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also given.As applications,we present the regularity properties for discrete fractional maximal operator,which are new even in the linear case.展开更多
The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variati...The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the Lp spaces.展开更多
基金supported by the Fund of National Science & Technology monumental projects under Grants No.2012ZX03005012,No. 2011ZX03005-004-03,No.2009ZX03003-007
文摘Image definition measurement plays an important role in various image processing applications.And a reliable objective image definition metrics is critical for evaluating the definition of the restored image.In this paper,a novel image distortion metric based on minimal Total Bounded Variation(TBV) is presented.It is clarified that when the restored image approximates to the original clear image,the smaller the TBV is,the better the definition of the restored image is.Furthermore,the difference between the restored image and the original clear image is the smallest when the TBV is minimum.In numerical results,the TBV of the original clear image,blur image and restored image are presented and compared,and the results demonstrate the validity of the distortion metric proposed.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371295, 11471041 and 11526122)Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (Grant No. 2015RCJJ053)+2 种基金Research Award Fund for Outstanding Young Scientists of Shandong Province (Grant No. BS2015SF012)Outstanding Young Scientific and Technological Top-Notch Talents of College of Mathematics and Systems Science (Grant No. Sxy2016K01)Natural Science Foundation of Fujian Province of China (Grant No. 2015J01025)
文摘We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）×l^1（Z^d）×…×l^1（Z^d）to BV（Z^d）,where BV（Z^d）is the set of functions of bounded variation defined on Zd.Moreover,two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also given.As applications,we present the regularity properties for discrete fractional maximal operator,which are new even in the linear case.
基金the National Natural Science Foundation of China (No.10571040)
文摘The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the Lp spaces.
