Higher Order Variational Models And Algorithms For Image Recovery And Pan-sharpening

Image recovery and pan-sharpening are key issues in image processing,computer vision,and multisource remotely sensed image fusion,which are the basis of patter recognition and high-level image analysis,and have been widely used in the fields of industry,medicine,public security,satellite remote sensing,military security,and so on.However,as a highly ill-posed problem,image recovery and pan-sharpening also bring huge difficulty and challenge for researchers and engineers.Recently,image prior-based variational regularization method has been an effective way to address image processing problems,where its core is how to build suitable and effective image prior models.As for these image prior models,they should effectively preserve image edges and textures as well as reduce staircase effects and ringing effects,and adequately exploit the geometric structures of high resolution(HR)panchromatic(PAN)image as well as effectively preserve the spectral information of low resolution(LR)multispectral(MS)image especially for pan-sharpening so as to improve the spatial resolution of MS image and fuse the complementary feature information between PAN image and MS image.In this dissertation,we mainly focus on image prior model-based image recovery and pan-sharpening problems.Regarding to the current first-order image prior models which easily casue heavy staircase effects and also lack the full exploitation of high-level image geometric information,we mainly research staircase effects surpression-,edge preservation-,and complementary feature fusion-based higher order image modeling methods,and hence propose higher order variational regularization models and their efficient algorithms for image recovery and pan-sharpening.The main contributions are listed as follows:(1)By investigating the modeling mechanism of higher order total variation(TV)regularization,we give an equivalent formulation of higher order TV,and then use it to make research as follows:Firstly,we propose a decoupled-based fast image recovery algorithm for higher order TV regularization model,and also give the convergence proof of the proposed algorithm.Secondly,we propose a variational model for multiplicative noise removal under the framework of equivalent formulation of higher order TV,and design its fast alternative iterative algorithm,and particularly give the convergence proof of the proposed algorithm.Finally,by comparing with the TV and state-of-the-art higher order methods,experimental results show that the proposed method can provide better recovery results in terms of visual evaluation,objective assessment and even convergence speed.More specifically,the proposed method can effectively suppress the staircase effects and at the same time still preserve some sharp edges.(2)By generalizing the TV and higher order TV models,we propose a novel first-order-and second-order-based mixed higher order TV regularization model for image recovery.Firstly,we analyze the equivalent formulation of mixed higher order TV under the spectral decomposition framework.Owing to the resulting equivalent formulation of mixed higher order TV,we design an efficient monotone fast iterative shrinkage thresholding algorithm(MFISTA)derived from the majorization minimization(MM)framework to solve the proposed model.Finally,the experimental comparisons with the TV and state-of-the-art higher order methods show that the proposed method not only can better suppress the staircase effects,but also better preserve sharp edges and structure details.(3)A novel spatial Hessian feature guided variational pan-sharpening model is proposed to fuse a LR MS image and a HR PAN image into a HR MS image.The proposed model contains a novel structure guided regularization term and a spectral data fidelity term,where the structure guided term exploits the vectorial Hessian Frobenius norm(VHFN)to measure the higher order geometric feature consistence between the latent HR MS image and the observed HR PAN image;and the data fidelity term comprehensively uses the data-dependency between the latent HR MS image and the observed LR MS image to preserve spectral information.Specifically,a fast and efficient algorithm for the proposed model can be designed under the operator splitting framework.Finally,experimental results on both simulated data and real data show that the proposed method can better balance spectral information preserving and spatial information preserving than various well-known pan-sharpening methods in terms of producing pan-sharpened results with higher spectral and spatial qualities,namely,much less spectral distortion,blocky and blurry artifacts.(4)A new geometry enforcing variational model is proposed for pan-sharpening.In particular,the proposed model uses the novel vectorial Hessian feature consistence in the three-dimensional differential surface as a measurement to transfer the high-level geometric information(such as,curvature)of the PAN image into the HR MS image.Meanwhile,the proposed model comprehensively adopts the data-dependency of the observation model and the multi-scale wavelet fusion fidelity to reduce spectral distortion.Under the fast iterative shrinkage thresholding algorithm(FISTA)framework,we design an efficient algorithm to solve the proposed model.Finally,experimental results show that the proposed method outperforms various well-known pan-sharpening methods in terms of both objective assessment and computational efficiency.In addition to better preserving spectral information,the proposed method is also able to eliminate some undesired blocky or blurry artifacts by incorporating the curvature information.