11 accepted papers
Gridless direction-of-arrival (DOA) estimation with multiple frequencies can be applied to acoustic source localization. We formulate this as an atomic norm minimization (ANM) problem and derive a regularization-free semi-definite program (SDP) avoiding regularization bias. We also propose a fast SD…
Direction of Arrival (DOA) estimation is widely applied in acoustic source localization. A multi-frequency model is suitable for characterizing the broadband structure in acoustic signals. In this work, we solve the continuous (gridless) line spectrum estimation problem by incorporating the multi-fr…
Low-rank matrix factorization is a problem of broad importance, owing to the ubiquity of low-rank models in machine learning contexts. In spite of its non- convexity, this problem has a well-behaved geometric landscape, permitting local search algorithms such as gradient descent to converge to globa…
Blind deconvolution and phase retrieval are both fundamental problems with a growing interest in signal processing and communications. In this work, we consider the task of simultaneous blind deconvolution and phase retrieval. We show that this non-linear problem can be reformulated as a low-rank te…
In this paper, we consider a general sparse recovery and blind demodulation model. Different from the ones in the literature, in our general model, each dictionary atom undergoes a distinct modulation process; we refer to this as non-stationary modulation. We also assume that the modulation matrices…
A variety of unconstrained nonconvex optimization problems have been shown to have benign geometric landscapes that satisfy the strict saddle property and have no spurious local minima. We present a general result relating the geometry of an unconstrained centralized problem to its equality-constrai…
The landscape of empirical risk has been widely studied in a series of machine learning problems, including low-rank matrix factorization, matrix sensing, matrix completion, and phase retrieval. In this work, we focus on the situation where the corresponding population risk is a degenerate non-conve…
Identifying characteristic vibrational modes and frequencies is of great importance for monitoring the health of structures such as buildings and bridges. In this work, we address the problem of estimating the modal parameters of a structure from small amounts of vibrational data collected from wire…
In this paper, we provide a dictionary for representing the discrete vector one obtains when collecting a finite set of uniform samples from a baseband analog signal. Like the discrete prolate spheroidal sequences (DPSS's), the proposed orthogonal basis compactly captures most of the energy in overs…
Frequency estimation is a classical problem in signal processing, with applications ranging from sensor array processing to wireless communications and structural health monitoring. Modern algorithms based on atomic norm minimization can cope with missing data but incur a high computational cost. To…
In this paper, we propose a new framework for parameter estimation of complex exponentials from their modulations with unknown waveforms via convex programming. Our model generalizes the recently developed blind sparse spike deconvolution framework by Y. Chi [1] to the non-stationary scenario and en…