Using of the Moore-Penrose inverse matrix in image restoration

  • Igor Stojanovic
  • Predrag Stanimirovic
  • Marko Miladinovic


A method for digital image restoration, based on the Moore-Penrose inverse matrix, has many practical applications. We apply the method to remove blur in an image caused by uniform linear motion. This method assumes that linear motion corresponds to an integral number of pixels. Compared to other classical methods, this method attains higher values of the Improvement in Signal to Noise Ratio (ISNR) parameter and of the Peak Signal-to-Noise Ratio (PSNR), but a lower value of the Mean Square Error (MSE). We give an implementation in the MATLAB programming package.




J. Biemond, R. L. Lagendijk, and R. M. Mersereau (1990): Iterative methods for image deblurring. Proc. IEEE, 78(5), pp. 856–883.

A. Bovik (2009): The essential guide to the image processing. Academic Press.

R. C. Gonzalez, R. E. Woods (2002): Digital Image Processing, 2nd Edition. Prentice-Hall.

I. Stojanovic, P. Stanimirovic and M. Miladinovic (2012): Applying the Algorithm of Lagrange Multipliers in Digital Image Restoration. FACTA UNIVERSITATIS, Series Mathematics and Informatics, ISSN 0352-9665, Vol. 27, No 1, pp. 41-54.

S. Chountasis, V. N. Katsikis and D. Pappas (2009): Applications of the Moore-Penrose Inverse in Digital Image Restoration. Mathematical Problems in Engineering, Volume 2009.

A. M. Eskicioglu and P. S. Fisher (1995): Image Quality Measures and Their Performance. IEEE Transactions on Communications, vol. 43, pp. 2959-2965.

Z. Wang and A. C. Bovik (2009): Mean Squared Error: Love It or Leave It? A New Look at Signal Fidelity Measures. IEEE Signal Processing Magazine, vol. 26, no. 1, pp. 98-117.