An efficient, approximate path-following algorithm for elastic net based nonlinear spike enhancement

Unwanted spike noise in a digital signal is a common problem in digital filtering. However, sometimes the spikes are wanted and other, superimposed, signals are unwanted, and linear, time invariant (LTI) filtering is ineffective because the spikes are wideband - overlapping with independent noise in the frequency domain. So, no LTI filter can separate them, necessitating nonlinear filtering. However, there are applications in which the noise includes drift or smooth signals for which LTI filters are ideal. We describe a nonlinear filter formulated as the solution to an elastic net regularization problem, which attenuates band-limited signals and independent noise, while enhancing superimposed spikes. Making use of known analytic solutions a novel, approximate path-following algorithm is given that provides a good, filtered output with reduced computational effort by comparison to standard convex optimization methods. Accurate performance is shown on real, noisy electrophysiological recordings of neural spikes

Revisiting the Linear Prediction Analysis-by-Synthesis Speech Coding Paradigm using Real-time Convex Optimization

In this work, we propose a novel approach to speech coding by rewriting the nonlinear analysis-by-synthesis linear prediction scheme as a convex problem. This allows for determining trade-offs between, on one hand, the reconstruction error and, on the other, the sparsity of the predictor and the residual used to parametrize the speech signal. Differently from traditional coding schemes where the parameters are chosen throughout multiple optimization stages, our scheme produces a one-shot parametrization of a speech segment that intrinsically takes into consideration the voiced or unvoiced nature of a speech segment providing a better balance between residual and predictor and, consequently, a more appropriate bit allocation