Abstract
The higher order orthogonal iteration (HOOI) is used for a single-frame and multi-frame space-variant blind deconvolution (BD) performed by factorization of the tensor of blurred multi-spectral image (MSI). This is achieved by conversion of BD into blind source separation (BSS), whereupon sources represent the original image and its spatial derivatives. The HOOI-based factorization enables an essentially unique solution of the related BSS problem with orthogonality constraints imposed on factors and the core tensor of the Tucker3 model of the image tensor. In contrast, the matrix factorization-based unique solution of the same BSS problem demands sources to be statistically independent or sparse which is not true. The consequence of such an approach to BD is that it virtually does not require a priori information about the possibly space-variant point spread function (PSF): neither its model nor size of its support. For the space-variant BD problem, MSI is divided into blocks whereupon the PSF is assumed to be a space-invariant within the blocks. The success of proposed concept is demonstrated in experimentally degraded images: defocused single-frame gray scale and red-green-blue (RGB) images, single-frame gray scale and RGB images blurred by atmospheric turbulence, and a single-frame RGB image blurred by a grating (photon sieve). A comparable or better performance is demonstrated in relation to the blind Richardson-Lucy algorithm which, however, requires a priori information about parametric model of the blur.
Highlights
Various artifacts such as defocusing, atmospheric turbulence, relative motion between image and object planes, aberrations, etc. can lead to blurry images and the loss of spatial information
The higher order orthogonal iteration (HOOI)-based tensor factorization approach has been proposed for the space-(in)variant model-free blind deconvolution of a single- and multi-frame multi-spectral image
This is achieved by converting blind deconvolution into blind source separation using the implicit Taylor expansion of the original image in the convolution image-forming equation
Summary
Various artifacts such as defocusing, atmospheric turbulence, relative motion between image and object planes, aberrations, etc. can lead to blurry images and the loss of spatial information. I propose higher order orthogonal iteration (HOOI)-based tensor factorization [18,19], for model-free space-variant blind deconvolution of single-frame (static) and/or multi-frame (dynamic) multi-spectral image. HOOI-based tensor factorization enables an essentially unique solution of the related blind source separation problem (up to standard scaling and permutation indeterminacies [27,28]), with orthogonality constraints imposed on factors and the core tensor of the Tucker model of the of the multichannel image tensor. In an adopted approach to blind deconvolution where sources represent an original image and its spatial derivatives, these constraints are not fulfilled This constraints-relaxed solution of model-free blind deconvolution that evolves due to the use of tensor factorization is another contribution of this paper that represents distinct improvement of the previous results [5,17]. The reason is that orthogonality constraints, imposed by HOOI algorithm on the core tensor and array factors in tensor model [Eq (1)], and nonnegativity constraints cannot be satisfied simultaneously
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