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
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
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.
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.
