A Fast Prediction-Error Detector for Estimating Sparse-Spike Sequences

Based on the maximum likelihood principle, we develop a locally optimal method for detecting the location and estimating the amplitude of spikes in a sequence, which is considered as the random input of a known ARMA system. A Bernoulli-Gaussian product model is adopted for the sparse-spike sequence, and the available data consist of a single, noisy, output record. By employing a prediction-error formulation, our iterative algorithm guarantees the increase of a unique likelihood function used for the combined estimation/detection problem. Amplitude estimation is carried out with Kalman smoothing techniques, and event detection is performed in two ways, as an event adder and as an event remover. Under certain assumptions, event and amplitude estimators converge to their true values, as the signal-to-noise ratio tends to infinity. Synthetic examples verify that our algorithm is self-initialized, consistent, and fast.