Inverse problems abound in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal & image processing approaches -such as sparsity-driven techniques -to determine their solution. This paper instead studies the use of deep learning approaches to approximate the solution of inverse problems. In particular, the paper provides a new generalization bound, depending on key quantity associated with a deep neural networkits Jacobian matrix -that also leads to a number of computationally efficient regularization strategies applicable to inverse problems The paper also tests the proposed regularization strategies in a number of inverse problems including image super-resolution ones. Our numerical results conducted on various datasets show that both fully connected and convolutional neural networks regularized using the regularization or proxy regularization strategies originating from our theory exhibit much better performance than deep networks regularized with standard approaches such as weight-decay.
This paper presents a multi-level compress and forward coding scheme for a three-node relay network in which all transmissions are constrained to be from an M -ary PAM constellation. The proposed framework employs a uniform scalar quantizer followed by Slepian-Wolf coding at the relay. We first obtain a performance benchmark for the proposed scheme by deriving the corresponding information theoretical achievable rate. A practical coding scheme involving multi-level codes is then discussed. At the source node, we use multi-level lowdensity parity-check codes for error protection. At the relay node, we propose a multi-level distributed joint source-channel coding scheme that uses irregular repeat-accumulate codes, the rates of which are carefully chosen using the chain rule of entropy. For a block length of 2 × 10 5 symbols, the proposed scheme operates within 0.56 and 0.63 dB of the theoretical limits at transmission rates of 1.0 and 1.5 bits/sample, respectively.
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