  We present a model for non-blind image deconvolution that incorporates the
classic iterative method into a deep learning application. Instead of using
large over-parameterised generative networks to create sharp picture
representations, we build our network based on the iterative Landweber
deconvolution algorithm, which is integrated with trainable convolutional
layers to enhance the recovered image structures and details. Additional to the
data fidelity term, we also add Hessian and sparse constraints as
regularization terms to improve the image reconstruction quality. Our proposed
model is \textit{self-supervised} and converges to a solution based purely on
the input blurred image and respective blur kernel without the requirement of
any pre-training. We evaluate our technique using standard computer vision
benchmarking datasets as well as real microscope images obtained by our
enhanced depth-of-field (EDOF) underwater microscope, demonstrating the
capabilities of our model in a real-world application. The quantitative results
demonstrate that our approach is competitive with state-of-the-art non-blind
image deblurring methods despite having a fraction of the parameters and not
being pre-trained, demonstrating the efficiency and efficacy of embedding a
classic deconvolution approach inside a deep network.

Image and Video Processing;Computer Vision and Pattern Recognition