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
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
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.
The optimality criteria （OC） method and mathematical programming （MP） were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constrai...The optimality criteria （OC） method and mathematical programming （MP） were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constraints. The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion. The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method. Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints. To improve the resolution efficiency, the dual-quadratic programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space. A method called approximate scaling step was adopted to reduce computations and smooth the iterative process. Negative constraints were deleted to reduce the size of the optimization model. With MSC/Nastran software as structural solver and MSC/Patran software as developing platform, the sectional optimization software of frame structures was accomplished, considering stress and displacement constraints. The examples show that the efficiency and accuracy are improved.展开更多
在理想环境下,双双曲调频(dual hyperbolic frequency modulation,Dual-HFM)速度谱估计方法可得到高分辨率的连续多普勒估计结果。然而由多径、双目标环境引起的旁瓣干扰,削弱了速度谱方法抑制噪声的能力,影响目标参数估计。针对该方法...在理想环境下,双双曲调频(dual hyperbolic frequency modulation,Dual-HFM)速度谱估计方法可得到高分辨率的连续多普勒估计结果。然而由多径、双目标环境引起的旁瓣干扰,削弱了速度谱方法抑制噪声的能力,影响目标参数估计。针对该方法在多径、双目标等各种复杂水声环境中的应用,进行了深入的讨论,推导了多径、双目标造成的速度谱旁瓣位置,并提出了基于多帧信号的速度谱旁瓣抑制方法,利用另一维度信号空间中目标回波信息与多径杂波旁瓣的差异性,抑制了复杂水下环境中的速度谱旁瓣,并保留了速度谱计算量低的优点。通过数值仿真验证了所提方法的适用性,为低信噪比、多径、双目标环境下的多普勒估计提供了理论依据。展开更多
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
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
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
在TFT-LCD驱动的关键设计技术中,抖动算法FRC(frame rate control)是一种重要的技术。它能够用6 bit source的输出来达到8 bit full color(16.7 M colors)的显示效果,这样可以降低数据传输率以降低功耗,同时可以节省源驱动(Source Drive...在TFT-LCD驱动的关键设计技术中,抖动算法FRC(frame rate control)是一种重要的技术。它能够用6 bit source的输出来达到8 bit full color(16.7 M colors)的显示效果,这样可以降低数据传输率以降低功耗,同时可以节省源驱动(Source Driver,SD)芯片的面积。通过分析和实践,提出了针对用于平板电脑的Dual-Gate TFT-LCD屏和翻转方式,需要采用优化的FRC算法提高显示效果。在应用于平板电脑的dual-gate TFT-LCD屏的FRC方案中,分析了传统方案产生周期性竖线的原因,然后提出了改进方案,消除了竖线,提高了显示质量。最后,总结了FRC算法具体需要考虑的因素。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.
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.
基金Project supported by the National Natural Science Foundation of China(No. 10472003) the Natural Science Foundation of Beijing(No.3002002) the Science Foundation of Beijing Municipal Commission of Education(No.KM200410005019)
文摘The optimality criteria （OC） method and mathematical programming （MP） were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constraints. The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion. The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method. Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints. To improve the resolution efficiency, the dual-quadratic programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space. A method called approximate scaling step was adopted to reduce computations and smooth the iterative process. Negative constraints were deleted to reduce the size of the optimization model. With MSC/Nastran software as structural solver and MSC/Patran software as developing platform, the sectional optimization software of frame structures was accomplished, considering stress and displacement constraints. The examples show that the efficiency and accuracy are improved.
文摘在理想环境下,双双曲调频(dual hyperbolic frequency modulation,Dual-HFM)速度谱估计方法可得到高分辨率的连续多普勒估计结果。然而由多径、双目标环境引起的旁瓣干扰,削弱了速度谱方法抑制噪声的能力,影响目标参数估计。针对该方法在多径、双目标等各种复杂水声环境中的应用,进行了深入的讨论,推导了多径、双目标造成的速度谱旁瓣位置,并提出了基于多帧信号的速度谱旁瓣抑制方法,利用另一维度信号空间中目标回波信息与多径杂波旁瓣的差异性,抑制了复杂水下环境中的速度谱旁瓣,并保留了速度谱计算量低的优点。通过数值仿真验证了所提方法的适用性,为低信噪比、多径、双目标环境下的多普勒估计提供了理论依据。
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 the Emphasis Supported Subject Foundation of Shanxi Province（20055026） Supported by the Emphasis Science Foundation of Yuncheng University（20060103）
文摘在TFT-LCD驱动的关键设计技术中,抖动算法FRC(frame rate control)是一种重要的技术。它能够用6 bit source的输出来达到8 bit full color(16.7 M colors)的显示效果,这样可以降低数据传输率以降低功耗,同时可以节省源驱动(Source Driver,SD)芯片的面积。通过分析和实践,提出了针对用于平板电脑的Dual-Gate TFT-LCD屏和翻转方式,需要采用优化的FRC算法提高显示效果。在应用于平板电脑的dual-gate TFT-LCD屏的FRC方案中,分析了传统方案产生周期性竖线的原因,然后提出了改进方案,消除了竖线,提高了显示质量。最后,总结了FRC算法具体需要考虑的因素。
