Inverse Kernels for Fast Spatial Deconvolution

Deconvolution is an indispensable tool in image processing and computer vision. It commonly employs fast Fourier transform (FFT) to simplify computation. This operator, however, needs to transform from and to the frequency domain and loses spatial information when processing irregular regions. We propose an efficient spatial deconvolution method that can incorporate sparse priors to suppress noise and visual artifacts. It is based on estimating inverse kernels that are decomposed into a series of 1D kernels. An augmented Lagrangian method is adopted, making inverse kernel be estimated only once for each optimization process. Our method is fully parallelizable and its speed is comparable to or even faster than other strategies employing FFTs.