Application of the Least Squares Solutions in Image Deblurring

A new method for the reconstruction of blurred digital images damaged by separable motion blur is established. The main attribute of the method is based on multiple applications of the least squares solutions of certain matrix equations which define the separable motion blur in conjunction with known image deconvolution techniques. The key feature of the proposed algorithms is reflected in the fact that they can be used only in symbiosis with other image restoration algorithms.

[1]  S. Osher,et al.  Decomposition of images by the anisotropic Rudin‐Osher‐Fatemi model , 2004 .

[2]  Aggelos K. Katsaggelos,et al.  Digital image restoration , 2012, IEEE Signal Process. Mag..

[3]  Vasilios N. Katsikis,et al.  Digital Image Reconstruction in the Spectral Domain Utilizing the Moore-Penrose Inverse , 2010 .

[4]  B. John Oommen,et al.  Moment-Preserving Piecewise Linear Approximations of Signals and Images , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Blind Image Deconvolution : An Algorithmic Approach to Practical Image Restoration 1 , 1996 .

[6]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[7]  Moon Gi Kang,et al.  Super-resolution image reconstruction: a technical overview , 2003, IEEE Signal Process. Mag..

[8]  Rafael C. González,et al.  Local Determination of a Moving Contrast Edge , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Alan C. Bovik,et al.  The Essential Guide to Image Processing , 2009, J. Electronic Imaging.

[10]  Robert B. McGhee,et al.  Aircraft Identification by Moment Invariants , 1977, IEEE Transactions on Computers.

[11]  R. Hufnagel,et al.  Modulation Transfer Function Associated with Image Transmission through Turbulent Media , 1964 .

[12]  Deepa Kundur,et al.  Blind Image Deconvolution , 2001 .

[13]  Milan Sonka,et al.  Image pre-processing , 1993 .

[14]  Barmak Honarvar Shakibaei and Jan Flusser Image Deconvolution in the Moment Domain , 2014 .

[15]  Vasilios N. Katsikis,et al.  Image Reconstruction Methods for MATLAB Users - A Moore-Penrose Inverse Approach , 2012 .

[16]  Peyman Milanfar,et al.  A moment-based variational approach to tomographic reconstruction , 1996, IEEE Trans. Image Process..

[17]  R. Penrose A Generalized inverse for matrices , 1955 .

[18]  Joost van de Weijer,et al.  Least Squares and Robust Estimation of Local Image Structure , 2003, Scale-Space.

[19]  D. Pappas,et al.  Image deblurring process based on separable restoration methods , 2014 .

[20]  P. Maher Some operator inequalities concerning generalized inverses , 1990 .

[21]  Vasilios N. Katsikis,et al.  Applications of the Moore-Penrose Inverse in Digital Image Restoration , 2009 .

[22]  M. Teague Image analysis via the general theory of moments , 1980 .

[23]  Igor Stojanovic,et al.  Removal of blur in images based on least squares solutions , 2013 .