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Compressive speech enhancement (CSE) has gained popularity in recent years as it bypasses the need for noise estimation. Parallel to that, modulation domain has been widely studied in speech applications as it offers a more compact representation and is closely associated with speech intelligibility enhancement. Motivated by the development in modulation domain and CSE, this paper seeks to explore the suitability of modulation domain based sparse reconstruction for use in CSE. The main idea is to study if the increased sparsity in the modulation domain would benefit sparse reconstruction in CSE. The findings reveal that modulation transformation is sparser and offers a stronger restricted isometry property (RIP) compared to the frequency transformation, which is essential for sparse recovery with a high probability. The results are then extended to show that the sparse reconstruction error in the modulation domain is upper bounded by the frequency domain. Experimental results in a CSE setting concur with the theoretical derivations, with modulation domain CSE outperforming the frequency domain CSE through different speech quality measures. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

Highlights: [•] Proposed a new method, which exploits the sparsity assumption in com-pressed sensing to perform speech enhancement. [•] Compressive speech enhancement recovers only the sparse components which in this case is speech. [•] Theoretical derivations show improvement in terms of signal to noise ratio. [•] No voice activity detector or a noise statistics estimator is needed. [Copyright &y& Elsevier]