Deep neural networks provide excellent performance for inverse problems such as denoising. However, neural networks can be sensitive to adversarial or worst-case perturbations. This raises the question of whether such networks can be trained efficiently to be worst-case robust.

Each voxel in a diffusion MRI (dMRI) image contains a spherical signal corresponding to the direction and strength of water diffusion in the brain.

Our nonconvex optimization formulation solves for a filter h on the unit sphere that produces sparse outputyi ~h.

This is an idealization of the usual way to train neural networks with a large hidden layer.

The proposed neural network is motivated by the low-rank property of pseudo-inverse kernels.

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Inspired by prior works in the domain of signal deconvolution [22, 9, 13], we are motivated to design a GDNbyaninverseoperation ofthelowpassfiltersembodied inGCNs.

Then, a deep neural network called GKMNet is developed by unrolling a fixed-point iteration of the GKM-based deblurring.