Fast space-varying convolution and its application in stray light reduction

Space-varying convolution often arises in the modeling or restoration of images captured by optical imaging systems. For example, in applications such as microscopy or photography the distortions introduced by lenses typically vary across the field of view, so accurate restoration also requires the use of space-varying convolution. While space-invariant convolution can be efficiently implemented with the Fast Fourier Transform (FFT), space-varying convolution requires direct implementation of the convolution operation, which can be very computationally expensive when the convolution kernel is large. In this paper, we develop a general approach to the efficient implementation of space-varying convolution through the use of matrix source coding techniques. This method can dramatically reduce computation by approximately factoring the dense space-varying convolution operator into a product of sparse transforms. This approach leads to a tradeoff between the accuracy and speed of the operation that is closely related to the distortion-rate tradeoff that is commonly made in lossy source coding. We apply our method to the problem of stray light reduction for digital photographs, where convolution with a spatially varying stray light point spread function is required. The experimental results show that our algorithm can achieve a dramatic reduction in computation while achieving high accuracy.