Outer Product Expansions and Their Uses in Digital Image Processing
- 1 February 1976
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Computers
- Vol. C-25 (2), 140-148
- https://doi.org/10.1109/tc.1976.5009228
Abstract
This paper is intended as a tutorial review of certain digital image processing transform techniques utilizing the notion of outer product expansions. Examples from Fourier, Walsh, Haar, and other well known transforms are reviewed in the notation of matrix-vector outer products; and implementation of the singular value decomposition (SVD) of large sized images is presented. The use of the SVD as an aid in image restoration utilizing the pseudoinverses is presented. Conditions on the point spread matrix are investigated in the light of singular value decomposition, Kronecker products, and general imaging conditions.Keywords
This publication has 19 references indexed in Scilit:
- On the Numerical Solution of Ill-Conditioned Linear Systems with Applications to Ill-Posed ProblemsSIAM Journal on Numerical Analysis, 1973
- A Numerical Algorithm for Identifying Spread Functions of Shift-Invariant Imaging SystemsIEEE Transactions on Computers, 1973
- Transform picture codingProceedings of the IEEE, 1972
- Image processing in the context of a visual modelProceedings of the IEEE, 1972
- Image restoration: The removal of spatially invariant degradationsProceedings of the IEEE, 1972
- A Numerical Method for Solving Fredholm Integral Equations of the First Kind Using Singular ValuesSIAM Journal on Numerical Analysis, 1971
- Comparison of line-by-line and two-dimensional encoding of random imagesIEEE Transactions on Information Theory, 1971
- The Design of Multistage Separable Planar FiltersIEEE Transactions on Geoscience Electronics, 1971
- Image processingProceedings of the IEEE, 1971
- A Note on the Variance of a MatrixEconometrica, 1968