2021/11/11 by Samuel Pinilla, Pinilla, Samuel, Kumar Vijay Mishra +3 · 1 citation
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Electrical engineering #Image and Signal Denoising Methods #Machine Learning (stat.ML) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2111.06479
openalex publication_date 2021/11/11 · openalex created_date 2022/10/27 · openalex updated_date 2026/07/28
Retrieving a signal from its triple correlation spectrum, also called\nbispectrum, arises in a wide range of signal processing problems. Conventional\nmethods do not provide an accurate inversion of bispectrum to the underlying\nsignal. In this paper, we present an approach that uniquely recovers signals\nwith finite spectral support (band-limited signals) from at least 3B\nmeasurements of its bispectrum function (BF), where B is the signal's\nbandwidth. Our approach also extends to time-limited signals. We propose a\ntwo-step trust region algorithm that minimizes a non-convex objective function.\nFirst, we approximate the signal by a spectral algorithm and then refine the\nattained initialization based on a sequence of gradient iterations. Numerical\nexperiments suggest that our proposed algorithm is able to estimate\nband-/time-limited signals from its BF for both complete and undersampled\nobservations.\n