NDLI: Fast Space-Varying Convolution Using Matrix Source Coding With Applications to Camera Stray Light Reduction

Content Provider	IEEE Xplore Digital Library
Author	Jianing Wei Bouman, C.A. Allebach, J.P.
Copyright Year	1992
Abstract	Many imaging applications require the implementation of space-varying convolution for accurate restoration and reconstruction of images. Here, we use the term space-varying convolution to refer to linear operators whose impulse response has slow spatial variation. In addition, these space-varying convolution operators are often dense, so direct implementation of the convolution operator is typically computationally impractical. One such example is the problem of stray light reduction in digital cameras, which requires the implementation of a dense space-varying deconvolution operator. However, other inverse problems, such as iterative tomographic reconstruction, can also depend on the implementation of dense space-varying convolution. While space-invariant convolution can be efficiently implemented with the fast Fourier transform, this approach does not work for space-varying operators. So direct convolution is often the only option for implementing space-varying convolution. In this paper, we develop a general approach to the efficient implementation of space-varying convolution, and demonstrate its use in the application of stray light reduction. Our approach, which we call matrix source coding, is based on lossy source coding of the dense space-varying convolution matrix. Importantly, by coding the transformation matrix, we not only reduce the memory required to store it; we also dramatically reduce the computation required to implement matrix-vector products. Our algorithm is able to reduce computation by approximately factoring the dense space-varying convolution operator into a product of sparse transforms. Experimental results show that our method can dramatically reduce the computation required for stray light reduction while maintaining high accuracy.
Sponsorship	IEEE Signal Processing Society
Page Count	15
File Size	3909136
Starting Page	1965
Ending Page	1979
File Format	PDF
ISSN	10577149
Volume Number	23
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sparse matrices Convolution Wavelet transforms Approximation methods Source coding Stray light digital photography space-varying point spread function image restoration fast algorithm inverse problem
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

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