A New Image Restoration Technique Based on Fast Tensor Preconditioning and Iterative Filtering

Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e. g. , Gaussian noise, impulse noise, deadlines, stripes, and many others. Such complex noise could degrade the quality of the acquired HSIs. Image restoration is one of the main parts of image processing. Mathematically, this problem can be modeled as a large scale structured ill-posed linear system. Ill-posedness of this problem results in low convergence rate of iterative solvers. For speeding up the convergence, preconditioning usually is used. We show that the higher order singular value decomposition (HOSVD) of the blurring tensor is obtained very fast and so could be used as a preconditioner. Iterative median filtering for restoration of images corrupted by mixed noise is considered. A median filtering that can be applied iteratively is also proposed. The boundary condition for the iteration is based on minimum distance between any two successive iterations is less than a threshold value. Experimental results show that proposed system has higher convergence speed. The complexity of an image restoration process reduces highly further we measures Peak Signal Noise Ratio (PSNR) and Mean Square Error (MSE). The PSNR values appear to be high while the MSE values appear to be low.