Hyper-parameterization of sparse reconstruction for speech enhancement

The regularized least squares for sparse reconstruction is gaining popularity as it has the ability to reconstruct speech signal from a noisy observation. The reconstruction relies on the sparsity of speech, which provides the demarcation from noise. However, there is no measure incorporated in the sparse reconstruction to optimize on the overall speech quality. This paper proposes a two-level optimization strategy to incorporate the quality design attributes in the sparse solution in compressive speech enhancement by hyper-parameterizing the tuning parameter. The first level involves the compression of the big data and the second level optimizes the tuning parameter by using different optimization criteria (such as Gini index, the Akaike information criterion (AIC) and Bayesian information criterion (BIC)). The set of solutions can then be measured against the desired design attributes to achieve the best trade-off between suppression and distortion. Numerical results show the proposed approach can effectively fuse the trade-offs in the solutions for different noise profile in a wide range of signal to noise ratios (SNR).