Violating Nyquist Sampling Theorem with Sparse Signal Reconstruction

Compressed sensing allows a sparse signal to be reconstructed by fewer measurements than the Nyquist criterion. In other words, a signal can be undersampled under the right constraints, which can then reduce the number of samples and sensors needed, thus saving hardware and processing resources.

However, the question largely unanswered is how sparse is considered to be sparse? More importantly, how will the sparsity change with different acoustic signals with varying degrees of non-stationarity?

This research will investigate the different measures to quantify the sparsity of acoustic signals and images for the purpose of sparse reconstruction.

The theoretical framework will then be used to develop improved sparse reconstruction methods, with the aim of improving the performance of compressive speech enhancement or compressive imaging. The applications for such methods can be used for speech recognition systems, smart home systems and surveillance analysis.