Adaptive Time–Frequency Peak Filtering Based on Convex Sets and the Viterbi Algorithm

The time-frequency peak filtering (TFPF) uses the instantaneous frequency estimation technique based on the Wigner-Ville distribution (WVD) to recover signal corrupted by random noise. TFPF is equivalent to a time-invariant low-pass filter whose impulse response is determined by the window function used in windowed WVD. Thus, TFPF cannot track the quick changes of signal, which means that the frequency components of signals higher than some cutoff frequency are attenuated. To solve this problem, we present a novel adaptive algorithm for TFPF. In this algorithm, we first construct the convex set of TFPF estimations at each sample index. Subsequently, we search the optimal estimations from the sequential convex sets to minimize a quadratic functional globally. This leads to a box-constrained convex optimization problem, which can be solved by the Viterbi algorithm. Applications to random seismic noise attenuation have demonstrated the validity of our algorithm with higher output signal-to-noise ratio and less signal information loss than in the traditional TFPF.