Deep Sparse Coding Using Optimized Linear Expansion of Thresholds
This work addresses sparse coding for signal processing applications, offering incremental improvements over existing algorithms.
The paper tackles sparse signal reconstruction from noisy compressive measurements by developing deep neural network architectures inspired by iterative shrinkage-thresholding algorithms, achieving a 3 to 4 dB improvement in reconstruction signal-to-noise ratio compared to state-of-the-art methods.
We address the problem of reconstructing sparse signals from noisy and compressive measurements using a feed-forward deep neural network (DNN) with an architecture motivated by the iterative shrinkage-thresholding algorithm (ISTA). We maintain the weights and biases of the network links as prescribed by ISTA and model the nonlinear activation function using a linear expansion of thresholds (LET), which has been very successful in image denoising and deconvolution. The optimal set of coefficients of the parametrized activation is learned over a training dataset containing measurement-sparse signal pairs, corresponding to a fixed sensing matrix. For training, we develop an efficient second-order algorithm, which requires only matrix-vector product computations in every training epoch (Hessian-free optimization) and offers superior convergence performance than gradient-descent optimization. Subsequently, we derive an improved network architecture inspired by FISTA, a faster version of ISTA, to achieve similar signal estimation performance with about 50% of the number of layers. The resulting architecture turns out to be a deep residual network, which has recently been shown to exhibit superior performance in several visual recognition tasks. Numerical experiments demonstrate that the proposed DNN architectures lead to 3 to 4 dB improvement in the reconstruction signal-to-noise ratio (SNR), compared with the state-of-the-art sparse coding algorithms.