Variational Regularization For CFA Image Demosaicking

A cost-effective digital camera uses a single sensor with a color filter array to capture only one of the three primary colors(red,green and blue)at each pixel location.Because of the mosaic pattern of the CFA,this interpolation process,which uses the spatial and spectral domain correlation to interpolate and obtain a full color image,has been known as color demosaicking(CDM).Image demosaicking is a basic research,and is the basis for image segmentation,image recognition and other follow-up study,so effective demosaicking algorithm has important scientific significance and practical value.In this paper,image demosaicking is regarded as image restoration problem.It is well known that image restoration is a typical ill-posed mathematical inverse problem,and the variational regularization method is a common and effective way to solve this problem.Based on the theory of image modeling,the following two demosaicking methods are proposed:(1)A robust CDM variational regularization model is proposed which combine the second-order features in spatial and spectral domain.The model contains a data fidelity term measured by the L1 norm,and a regularization term measured by a vectorized Hessian Frobenius norm(VHFN).Since the distortion in the CDM image is a small-scale structure,the CDM noise should be subject to the non-Gaussian heavy tailed distribution,which can be effectively modeled by Laplace distribution.Then the data fidelity term in LI norm is established.Under the maximum likelihood estimation,minimizing the L1 norm gives a robust estimate of the full color image.Furthermore,by using the VHFN regularization term to model the 3D full color image,it can characterize the high-order geometrical features of the image and capture the spectral correlation between different color channels.We use an efficient alternative direction multiplier method to solve the regularization problem.The experimental results show that the proposed method can reduce the color speckle effect and blurring while preserving the spectral information and spatial edge structure of the image.(2)A CDM variational regularization model based on nonlocal tensor representation is proposed.The model integrates sparse coding and dictionary learning into a variational framework.Similar non-local 2D blocks are clustered into a series of third-order tensors.For each third-order tensor,three sub-dictionaries can be learned adaptively by Tucker decomposition.Each sub-dictionary can describe the inner structure of different modes.The tensor coefficients are constrained by group-block-sparsity,so that similar blocks share the same atoms in the dictionary in their sparse decomposition.The experimental results show the effectiveness of our method in preserving the image structure.