The approximate GCD of inexact polynomials
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Enhanced Biggs---Andrews Asymmetric Iterative Blind Deconvolution
Multidimensional Systems and Signal Processing
Efficient recursive multichannel blind image restoration
EURASIP Journal on Applied Signal Processing
Fast communication: Robust estimation of GCD with sparse coefficients
Signal Processing
Blind image deconvolution via fast approximate GCD
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
The calculation of the degree of an approximate greatest common divisor of two polynomials
Journal of Computational and Applied Mathematics
Parallel QR processing of Generalized Sylvester matrices
Theoretical Computer Science
Blind image deconvolution using a banded matrix method
Numerical Algorithms
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In this correspondence, a new viewpoint is proposed for estimating an image from its distorted versions in presence of noise without the a priori knowledge of the distortion functions. In z-domain, the desired image can be regarded as the greatest common polynomial divisor among the distorted versions. With the assumption that the distortion filters are finite impulse response (FIR) and relatively coprime, in the absence of noise, this becomes a problem of taking the greatest common divisor (GCD) of two or more two-dimensional (2-D) polynomials. Exact GCD is not desirable because even extremely small variations due to quantization error or additive noise can destroy the integrity of the polynomial system and lead to a trivial solution. Our approach to this blind deconvolution approximation problem introduces a new robust interpolative 2-D GCD method based on a one-dimensional (1-D) Sylvester-type GCD algorithm. Experimental results with both synthetically blurred images and real motion-blurred pictures show that it is computationally efficient and moderately noise robust