Compressed Sensing (CS) can be used to reconstruct sparse vector from less number of measurements, provided the signal can be represented in sparse domain. Sparse domain is a domain in which only a few measurements have non-zero values. Suppose a signal
Consider a speech signal
The observed signal
where
Sparse decomposition problem for eq. 1 can be solved as standard
If measurement matrix
Different types of measurement matrices like random matrices can be used for speech signals. Estimating the sparsity of speech signal is a problem since speech signal highly varies over time and thus sparsity of speech signal also varies highly over time. If sparsity of speech signal can be calculated over time without much complexity that will be best. If this is not possible then worst-case scenario for sparsity can be considered for a given speech signal.
Sparse vector (
Estimation of both the dictionary matrix and sparse vector from just random measurements only has been done iteratively in. The speech signal reconstructed from estimated sparse vector and dictionary matrix is much closer to the original signal. Some more iterative approaches to calculate both dictionary matrix and speech signal from just random measurements of speech signal are shown in. Th application of structured sparsity for joint speech localization-separation in reverberant acoustics has been investigated for multiparty speech recognition. Further applications of the concept of sparsity are yet to be studied in the field of speech processing. The idea behind CS for speech signals is that can we come up with some algorithms or methods where we only use those random measurements (