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

• Published in: IEEE transactions on image processing Vol. 23; no. 5; pp. 1965 - 1979
• Main Authors: Jianing Wei, Bouman, Charles A., Allebach, Jan P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Approximation methods; Coding; Coding, codes; Computation; Convolution; Exact sciences and technology; Fourier transforms; Image processing; Information, signal and communications theory; Operators; Reconstruction; Reduction; Signal and communications theory; Signal processing; Source coding; Sparse matrices; Stray light; Telecommunications and information theory; Wavelet transforms; space-varying point spread function; inverse problem; digital photography; fast algorithm; image restoration; Stray light; Image processing; Source coding; Fast Fourier transformation; High precision; Matrix product; Lossy medium; Iterative method; Image restoration; Spatial variation; Linear operator; Digital photography; Point spread function; Implementation; Image reconstruction; Inverse problem; Deconvolution; Convolution; Pulse response; Imaging; Fast algorithm
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2014.2311657

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.