Adaptive Compressed Sensing of Speech Signals
- Manipal Reddy Kuchakuntla
Compressed Sensing (CS) is an emerging signal acquisition theory that provides a universal approach for characterizing signals which are sparse or compressible on some basis at sub-Nyquist sampling rate. Based on an over-complete data as the sparse basis specialized for speech signals, CS Sampling and reconstruction of speech signal are realized. Furthermore, we propose to choose the sensing matrix adaptively, according to the energy distribution of original speech signal. Experimental results show significant improvement of speech reconstruction quality by using such adaptive approach against traditional random sensing matrix. The key objective in compressed sensing (also referred to as sparse signal recovery or compressive sampling) is to reconstruct a signal accurately and efficiently from a set of few non-adaptive linear measurements.
The compressed sensing field has provided many recovery algorithms, most with provable as well as empirical results. There are several important traits that an optimal recovery algorithm must possess. The algorithm needs to be fast, so that it can efficiently recover signals in practice. The algorithm should provide uniform guarantees, meaning that given a specific method of acquiring linear measurements, the algorithm recovers all sparse signals (possibly with high probability). Ideally, the algorithm would require as few linear measurements as possible. However, recovery using only this property would require searching through the exponentially large set of all possible lower dimensional subspaces, and so in practice is not numerically feasible. Thus in the more realistic setting, we may need slightly more measurements. Finally, we wish our ideal recovery algorithm to be stable.
This means that if the signal or its measurements are perturbed slightly, then the recovery should still be approximately accurate. This is essential, since in practice we often encounter not only noisy signals or measurements, but also signals that are not exactly sparse, but close to being sparse. The conventional scheme in signal processing, acquiring the entire signal and then compressing it, was questioned by Donoho. Indeed, this technique uses tremendous resources to acquire often very large signals, just to throw away information during compression.
Volume 2 Issue 3
Pages. 3177-3181
