Deconvolution is quick with Fourier transforms. In infinite precision, convolution by any nonzero function (which includes Gaussian blurs) is invertible. In pra

Deconvolution is quick with Fourier transforms. In infinite precision, convolution by any nonzero function (which includes Gaussian blurs) is invertible. In practice, quantization and stopping the convolution at the edge of the blur region complicates things. The blur itself removes no information, if you want to convince yourself it's safe you need to argue numerical analysis. Check out "High Quality Motion Deblurring from a Single Image", for some quite impressive photo reconstruction done by actually fitting a spatially varying set of blur kernels to an image.