End-to-end Interpretable Learning of Non-blind Image Deblurring
This addresses the problem of efficient and accurate image deblurring for computer vision applications, with incremental improvements in speed and interpretability.
The paper tackled non-blind image deblurring by proposing a preconditioned Richardson solver with approximate inverse filters, which improved accuracy and speed compared to classical methods. The result was a fully interpretable, end-to-end learnable algorithm that matches or exceeds state-of-the-art accuracy, particularly in non-uniform cases.
Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients, which can be solved, for example, using a half-quadratic splitting method with Richardson fixed-point iterations for its least-squares updates and a proximal operator for the auxiliary variable updates. We propose to precondition the Richardson solver using approximate inverse filters of the (known) blur and natural image prior kernels. Using convolutions instead of a generic linear preconditioner allows extremely efficient parameter sharing across the image, and leads to significant gains in accuracy and/or speed compared to classical FFT and conjugate-gradient methods. More importantly, the proposed architecture is easily adapted to learning both the preconditioner and the proximal operator using CNN embeddings. This yields a simple and efficient algorithm for non-blind image deblurring which is fully interpretable, can be learned end to end, and whose accuracy matches or exceeds the state of the art, quite significantly, in the non-uniform case.