Plug-and-play priors are popular for solving illposed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-andplay priors relies on the assumption of bo...Plug-and-play priors are popular for solving illposed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-andplay priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual,which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering(BM3D)denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging(CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.展开更多
In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, whic...In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two diff erent general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix （not Gaussian） and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.展开更多
This paper is concerned with the characterization of the duals of wavelet frames of L(2)(R). The sufficient and necessary conditions for them are obtained.
We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nea...We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames. We intro- duce a new perturbation of controlled frames to obtain new frames from a given one. Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.展开更多
A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, ...A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.展开更多
Due to its potential applications in multiplexing techniques, the study of superframes has interested some researchers. This paper addresses dual super wavelet and Gabor frames in the subspace setting. We obtain a bas...Due to its potential applications in multiplexing techniques, the study of superframes has interested some researchers. This paper addresses dual super wavelet and Gabor frames in the subspace setting. We obtain a basic-equation characterization for subspace dual super wavelet and Gabor frames. In addition, applying this characterization, we derive a procedure that allows for constructing subspace dual super wavelet frames based on certain subspace dual super Gabor frames, and vice versa. Our results are new even in L^2(R, CL) setting.展开更多
This paper investigates the fine structure of the Gabor frame generated by the B-spline B<sub>3</sub>. In other words, one extends the known part of the Gabor frame set for the 3-spline with the constructi...This paper investigates the fine structure of the Gabor frame generated by the B-spline B<sub>3</sub>. In other words, one extends the known part of the Gabor frame set for the 3-spline with the construction of the compactly supported dual windows. The frame set of the function B<sub>3</sub> is the subset of all parameters (a,b) ∈R<sup>2</sup>+ </sub>for which the time-frequency shifts of B<sub>3</sub> along aZ × bZ form a Gabor frame for L<sup>2</sup>(R).展开更多
In this paper, firstly, in order to establish our main techniques we give a direct proof for the existence of the dilations for pairs of dual group frames. Then we focus on proving the uniqueness of such dilations in ...In this paper, firstly, in order to establish our main techniques we give a direct proof for the existence of the dilations for pairs of dual group frames. Then we focus on proving the uniqueness of such dilations in certain sense of similarity and giving an operator parameterization of the dilations of all pairs of dual group frames for a given group frame. We show that the operators which transform different dilations are of special structured lower triangular.展开更多
In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C＊-module 74, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to eac...In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C＊-module 74, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to each other, respectively. Using .A-valued linear bounded operator U ： H → l^2（.A）, V＊U = I, a coustructing method of dual weak frame {xj^＊ ： j ∈ H} for a given weak frame {Xj ： j ∈ J} is obtained. Moreover, pseudo frame decompositions for 74 is given.展开更多
Using operator-theoretic-methods, we give some characterizations for a dual generalized frame of a generalized frame in a separable Hilbert space H. We also prove a result concerning two strongly disjiont generalized ...Using operator-theoretic-methods, we give some characterizations for a dual generalized frame of a generalized frame in a separable Hilbert space H. We also prove a result concerning two strongly disjiont generalized frames.展开更多
A global dual frame （GDF） representation for the digital ridgelet reconstruction algorithm is discussed and a novel concept of local dual frame （LDF） is presented. Based on the properties of LDF, we propose a new ...A global dual frame （GDF） representation for the digital ridgelet reconstruction algorithm is discussed and a novel concept of local dual frame （LDF） is presented. Based on the properties of LDF, we propose a new digital ridgelet reconstruction algorithm. The method reduces the redundancy in the digital ridgelet reconstruction while keeping the characteristics of low computation cost. When applying it to the image compression and denoising, good results are obtained.展开更多
In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard gen...In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard generalized frames is a standard generalized frame.展开更多
基金supported in part by the National Natural Science Foundation of China (62371414,61901406)the Hebei Natural Science Foundation (F2020203025)+2 种基金the Young Talent Program of Universities and Colleges in Hebei Province (BJ2021044)the Hebei Key Laboratory Project (202250701010046)the Central Government Guides Local Science and Technology Development Fund Projects(216Z1602G)。
文摘Plug-and-play priors are popular for solving illposed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-andplay priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual,which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering(BM3D)denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging(CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.
基金Supported by the National Natural Science Foundation of China(11171299 and 91130009)
文摘In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two diff erent general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix （not Gaussian） and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.
文摘This paper is concerned with the characterization of the duals of wavelet frames of L(2)(R). The sufficient and necessary conditions for them are obtained.
文摘We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames. We intro- duce a new perturbation of controlled frames to obtain new frames from a given one. Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.
文摘A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.
基金supported by National Natural Science Foundation of China (Grant No. 11271037)
文摘Due to its potential applications in multiplexing techniques, the study of superframes has interested some researchers. This paper addresses dual super wavelet and Gabor frames in the subspace setting. We obtain a basic-equation characterization for subspace dual super wavelet and Gabor frames. In addition, applying this characterization, we derive a procedure that allows for constructing subspace dual super wavelet frames based on certain subspace dual super Gabor frames, and vice versa. Our results are new even in L^2(R, CL) setting.
文摘This paper investigates the fine structure of the Gabor frame generated by the B-spline B<sub>3</sub>. In other words, one extends the known part of the Gabor frame set for the 3-spline with the construction of the compactly supported dual windows. The frame set of the function B<sub>3</sub> is the subset of all parameters (a,b) ∈R<sup>2</sup>+ </sub>for which the time-frequency shifts of B<sub>3</sub> along aZ × bZ form a Gabor frame for L<sup>2</sup>(R).
文摘In this paper, firstly, in order to establish our main techniques we give a direct proof for the existence of the dilations for pairs of dual group frames. Then we focus on proving the uniqueness of such dilations in certain sense of similarity and giving an operator parameterization of the dilations of all pairs of dual group frames for a given group frame. We show that the operators which transform different dilations are of special structured lower triangular.
基金Supported by the Emphasis Supported Subject Foundation of Shanxi Province（20055026） Supported by the Emphasis Science Foundation of Yuncheng University（20060103）
文摘In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C＊-module 74, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to each other, respectively. Using .A-valued linear bounded operator U ： H → l^2（.A）, V＊U = I, a coustructing method of dual weak frame {xj^＊ ： j ∈ H} for a given weak frame {Xj ： j ∈ J} is obtained. Moreover, pseudo frame decompositions for 74 is given.
基金the National Natural Science Foundation of China (19771056)
文摘Using operator-theoretic-methods, we give some characterizations for a dual generalized frame of a generalized frame in a separable Hilbert space H. We also prove a result concerning two strongly disjiont generalized frames.
文摘A global dual frame （GDF） representation for the digital ridgelet reconstruction algorithm is discussed and a novel concept of local dual frame （LDF） is presented. Based on the properties of LDF, we propose a new digital ridgelet reconstruction algorithm. The method reduces the redundancy in the digital ridgelet reconstruction while keeping the characteristics of low computation cost. When applying it to the image compression and denoising, good results are obtained.
基金the National Natural Science Foundation of China （No. 10771101） and Chuangxin Funds of Nanjing University of Aeronautics and Astronautics （No. 987561）.
文摘In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard generalized frames is a standard generalized frame.
