In image restoration,we usually assume that the underlying image has a good sparse approximation under a certain system.Wavelet tight frame system has been proven to be such an efficient system to sparsely approximate...In image restoration,we usually assume that the underlying image has a good sparse approximation under a certain system.Wavelet tight frame system has been proven to be such an efficient system to sparsely approximate piecewise smooth images.Thus,it has been widely used in many practical image restoration problems.However,images from different scenarios are so diverse that no static wavelet tight frame system can sparsely approximate all of themwell.To overcome this,recently,Cai et.al.(Appl Comput Harmon Anal 37:89–105,2014)proposed a method that derives a data-driven tight frame adapted to the specific input image,leading to a better sparse approximation.The data-driven tight frame has been applied successfully to image denoising and CT image reconstruction.In this paper,we extend this data-driven tight frame construction method to multi-channel images.We construct a discrete tight frame system for each channel and assume their sparse coefficients have a joint sparsity.The multi-channel data-driven tight frame construction scheme is applied to joint color and depth image reconstruction.Experimental results show that the proposed approach has a better performance than state-of-the-art joint color and depth image reconstruction approaches.展开更多
The method of data-driven tight frame has been shown very useful in image restoration problems.We consider in this paper extending this important technique,by incorporating L_(1) data fidelity into the original data-d...The method of data-driven tight frame has been shown very useful in image restoration problems.We consider in this paper extending this important technique,by incorporating L_(1) data fidelity into the original data-driven model,for removing impulsive noise which is a very common and basic type of noise in image data.The model contains three variables and can be solved through an efficient iterative alternating minimization algorithm in patch implementation,where the tight frame is dynamically updated.It constructs a tight frame system from the input corrupted image adaptively,and then removes impulsive noise by the derived system.We also show that the sequence generated by our algorithm converges globally to a stationary point of the optimization model.Numerical experiments and comparisons demonstrate that our approach performs well for various kinds of images.This benefits from its data-driven nature and the learned tight frames from input images capture richer image structures adaptively.展开更多
Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of po...In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.展开更多
In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight fra...In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for L2 （JRa） by replacing some mother framelets.展开更多
We consider Gabor localization operators ?defined by two parameters, the generating function ?of a tight Gabor frame , indexed by a lattice , and a domain ?whose boundary consists of line segments connecting certain p...We consider Gabor localization operators ?defined by two parameters, the generating function ?of a tight Gabor frame , indexed by a lattice , and a domain ?whose boundary consists of line segments connecting certain points of . We provide an explicit formula for the boundary form , the normalized limit of the projection functional , where ?are the eigenvalues of the localization operators ?applied to dilated domains , R is an integer and is the area of the fundamental domain. The boundary form expresses quantitatively the asymptotic interactions between the generating function ?and the oriented boundary ?from the point of view of the projection functional, which measures to what degree a given trace class operator fails to be an orthogonal projection. Keeping the area of the localization domain ?bounded above corresponds to controlling the relative dimensionality of the localization problem.展开更多
<div style="text-align:justify;"> Digital watermarking technology plays a powerful role in the effective protection of digital media copyright, image authentication, image sharing, image information tr...<div style="text-align:justify;"> Digital watermarking technology plays a powerful role in the effective protection of digital media copyright, image authentication, image sharing, image information transmission and other fields. Driven by strong demand, digital image watermarking technology has aroused widespread research interest and has gradually developed into one of the most active research directions in information science. In this paper, we present a novel robust digital watermarking algorithm based on discrete radon transform tight frame in finite-set (FDRT). FDRT of the zero mean image is a tight frame, the frame boundary <em><strong>A</strong></em> = <em><strong>B</strong></em> = 1, the dual of the frame is itself. The decomposition and reconstruction of the FDRT tight frame will not cause the phenomenon of image distortion. The embedding of hidden watermark is to add a weak signal to the strong background of the original image. Watermark extraction is to effectively identify the embedded weak signal. The feasibility of the watermarking algorithm is analyzed from two aspects of information hiding and robustness. We select the independent Gaussian random vector as the watermark series, and the peak signal-to-noise ratio (PSNR) as the visual degradation criterion of the watermark image. Basing the FDRT compact stand dual operator, we derived the relationship among the strength parameter, square sum of watermark series, the PSNR. Using Checkmark system, the simulation results show that the algorithm is robust enough to some very important image processing attacks such as lossy compression, MAP, filtering, segmentation, edge enhancement, jitter, quadratic modulation and general geometric attack (scaling, rotation, shearing), etc. </div>展开更多
Tight gas sandstone reservoirs in Guang＇an are characterized by wide distribution and low abundance. Sandstone samples from this area usually have low porosity and poor connectivity. We analyze the observed velocity ...Tight gas sandstone reservoirs in Guang＇an are characterized by wide distribution and low abundance. Sandstone samples from this area usually have low porosity and poor connectivity. We analyze the observed velocity data of tight sandstone samples with the Mori- Tanaka model, and give the sandstone framework physical model in this area based on theory and experiment analysis. The matrix modulus was obtained by an empirical relationship and then the experiment data were compared with the values predicted by the Mori-Tanaka model with different pore shapes. The results revealed that the experiment data were close to the model with low pore aspect ratio. Considering the matrix modulus and pore shape variation, we find that, under the condition of small mineral composition change, the effective pore aspect ratio of these samples increased with porosity evidently.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 use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, ...The use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, experiments with a tight frame to analyze sparsity and reconstruction quality using several signal and image types are shown. The constant is used in fulfilling the definition of D-RIP. It is proved that k-sparse signals can be reconstructed if by using a concise and transparent argument1. The approach could be extended to obtain other D-RIP bounds (i.e. ). Experiments contrast results of a Gabor tight frame with Total Variation minimization. In cases of practical interest, the use of a Gabor dictionary performs well when achieving a highly sparse representation and poorly when this sparsity is not achieved.展开更多
基金Jian-Feng Cai is partially supported by the National Natural Science Foundation of USA(No.DMS 1418737).
文摘In image restoration,we usually assume that the underlying image has a good sparse approximation under a certain system.Wavelet tight frame system has been proven to be such an efficient system to sparsely approximate piecewise smooth images.Thus,it has been widely used in many practical image restoration problems.However,images from different scenarios are so diverse that no static wavelet tight frame system can sparsely approximate all of themwell.To overcome this,recently,Cai et.al.(Appl Comput Harmon Anal 37:89–105,2014)proposed a method that derives a data-driven tight frame adapted to the specific input image,leading to a better sparse approximation.The data-driven tight frame has been applied successfully to image denoising and CT image reconstruction.In this paper,we extend this data-driven tight frame construction method to multi-channel images.We construct a discrete tight frame system for each channel and assume their sparse coefficients have a joint sparsity.The multi-channel data-driven tight frame construction scheme is applied to joint color and depth image reconstruction.Experimental results show that the proposed approach has a better performance than state-of-the-art joint color and depth image reconstruction approaches.
基金supports from NSF of China grants 11531013 and 11871035.
文摘The method of data-driven tight frame has been shown very useful in image restoration problems.We consider in this paper extending this important technique,by incorporating L_(1) data fidelity into the original data-driven model,for removing impulsive noise which is a very common and basic type of noise in image data.The model contains three variables and can be solved through an efficient iterative alternating minimization algorithm in patch implementation,where the tight frame is dynamically updated.It constructs a tight frame system from the input corrupted image adaptively,and then removes impulsive noise by the derived system.We also show that the sequence generated by our algorithm converges globally to a stationary point of the optimization model.Numerical experiments and comparisons demonstrate that our approach performs well for various kinds of images.This benefits from its data-driven nature and the learned tight frames from input images capture richer image structures adaptively.
文摘Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
文摘In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.
文摘In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for L2 （JRa） by replacing some mother framelets.
文摘We consider Gabor localization operators ?defined by two parameters, the generating function ?of a tight Gabor frame , indexed by a lattice , and a domain ?whose boundary consists of line segments connecting certain points of . We provide an explicit formula for the boundary form , the normalized limit of the projection functional , where ?are the eigenvalues of the localization operators ?applied to dilated domains , R is an integer and is the area of the fundamental domain. The boundary form expresses quantitatively the asymptotic interactions between the generating function ?and the oriented boundary ?from the point of view of the projection functional, which measures to what degree a given trace class operator fails to be an orthogonal projection. Keeping the area of the localization domain ?bounded above corresponds to controlling the relative dimensionality of the localization problem.
文摘<div style="text-align:justify;"> Digital watermarking technology plays a powerful role in the effective protection of digital media copyright, image authentication, image sharing, image information transmission and other fields. Driven by strong demand, digital image watermarking technology has aroused widespread research interest and has gradually developed into one of the most active research directions in information science. In this paper, we present a novel robust digital watermarking algorithm based on discrete radon transform tight frame in finite-set (FDRT). FDRT of the zero mean image is a tight frame, the frame boundary <em><strong>A</strong></em> = <em><strong>B</strong></em> = 1, the dual of the frame is itself. The decomposition and reconstruction of the FDRT tight frame will not cause the phenomenon of image distortion. The embedding of hidden watermark is to add a weak signal to the strong background of the original image. Watermark extraction is to effectively identify the embedded weak signal. The feasibility of the watermarking algorithm is analyzed from two aspects of information hiding and robustness. We select the independent Gaussian random vector as the watermark series, and the peak signal-to-noise ratio (PSNR) as the visual degradation criterion of the watermark image. Basing the FDRT compact stand dual operator, we derived the relationship among the strength parameter, square sum of watermark series, the PSNR. Using Checkmark system, the simulation results show that the algorithm is robust enough to some very important image processing attacks such as lossy compression, MAP, filtering, segmentation, edge enhancement, jitter, quadratic modulation and general geometric attack (scaling, rotation, shearing), etc. </div>
基金supported by the National Natural Foundation of China (No. 41104066)the Basic Research Programs of CNPC during the 12th Five-Year Plan Period (No. 2011A-3601)+1 种基金the Major State Basic Research Development Program of China (No. 2007CB209505)RIPED Young Innovation Foundation (No. 2010-A-26-01)
文摘Tight gas sandstone reservoirs in Guang＇an are characterized by wide distribution and low abundance. Sandstone samples from this area usually have low porosity and poor connectivity. We analyze the observed velocity data of tight sandstone samples with the Mori- Tanaka model, and give the sandstone framework physical model in this area based on theory and experiment analysis. The matrix modulus was obtained by an empirical relationship and then the experiment data were compared with the values predicted by the Mori-Tanaka model with different pore shapes. The results revealed that the experiment data were close to the model with low pore aspect ratio. Considering the matrix modulus and pore shape variation, we find that, under the condition of small mineral composition change, the effective pore aspect ratio of these samples increased with porosity evidently.
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The use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, experiments with a tight frame to analyze sparsity and reconstruction quality using several signal and image types are shown. The constant is used in fulfilling the definition of D-RIP. It is proved that k-sparse signals can be reconstructed if by using a concise and transparent argument1. The approach could be extended to obtain other D-RIP bounds (i.e. ). Experiments contrast results of a Gabor tight frame with Total Variation minimization. In cases of practical interest, the use of a Gabor dictionary performs well when achieving a highly sparse representation and poorly when this sparsity is not achieved.
