We develop a low-rank approach for image restoration by exploiting the image’s nonlocal self-similarity. We assume that the matrix stacked by the vectors of nonlocal similar patches is of low rank and has sparse singular values. Based on this assumption, we propose a new image deconvolution algorithm that decouples the deblurring and denoising steps. Specifically, in the deblurring step, we involve a regularized inversion of the blur in the Fourier domain, which amplifies and colors the noise and corrupts the image information. Hence, in the denoising step, a singular-value decomposition of similar packed patches is used to efficiently remove the colored noise. Furthermore, we derive an approach to update the estimation of noise variance for setting the threshold parameter at each iteration. Experimental results clearly show that the proposed algorithm outperforms many state-of-the-art deblurring algorithms such as iterative decoupled deblurring BM3D in terms of both improvement in signal-to-noise-ratio and visual perception quality.
In this paper, a new approach to objectively assess the performance of image fusion algorithms is proposed. It is based
on the quaternion representation for the structural information of color images. Quaternions are used to encode the pixels
of a color image into a quaternion matrix. Local variance of the luminance layer of color image is taken as the real part
of a quaternion, then the three RGB channels of the color image are encoded into the three imaginary parts of the
quaternion. The angle between the singular value feature vectors of the quaternion matrices corresponding to the source
image and the fused image is used to measure the structural similarity of them. Different weight is given to the source
images by using variance. The experiment results show that the proposed assessment method is consistent with the HVS.
The color information of a color image can be fully used by this method. It can give an accurate assessment result for
each fusion algorithm by using the source images and the fused image.
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