Long reconstruction times of compressed sensing problems can be reduced with the help of preconditioning techniques. Efficient preconditioners are often not straightforward to design. In this work, we explore the feasibility of designing a preconditioner with a neural network. We integrate the learned preconditioner in a classical reconstruction framework, Split Bregman, and compare its performance to an optimized circulant preconditioner. Results show that it is possible for a learned preconditioner to meet and slightly improve upon the performance of existing preconditioning techniques. Optimization of the training set and the network architecture is expected to improve the performance further.
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