Spectral Compressed Sensing via CANDECOMP/PARAFAC Decomposition of Incomplete Tensors

TL;DR

This paper introduces a novel tensor decomposition approach for line spectral estimation that overcomes discretization errors, enabling super-resolution of frequency components with high accuracy from limited samples.

Contribution

It proposes a new method using CP tensor decomposition with missing data for super-resolving frequencies, improving estimation precision over traditional compressed sensing techniques.

Findings

Achieves super-resolution with infinite precision due to CP decomposition uniqueness.

Provides competitive accuracy compared to state-of-the-art algorithms.

Handles incomplete data effectively through tensor organization.

Abstract

We consider the line spectral estimation problem which aims to recover a mixture of complex sinusoids from a small number of randomly observed time domain samples. Compressed sensing methods formulates line spectral estimation as a sparse signal recovery problem by discretizing the continuous frequency parameter space into a finite set of grid points. Discretization, however, inevitably incurs errors and leads to deteriorated estimation performance. In this paper, we propose a new method which leverages recent advances in tensor decomposition. Specifically, we organize the observed data into a structured tensor and cast line spectral estimation as a CANDECOMP/PARAFAC (CP) decomposition problem with missing entries. The uniqueness of the CP decomposition allows the frequency components to be super-resolved with infinite precision. Simulation results show that the proposed method provides a competitive estimate accuracy compared with existing state-of-the-art algorithms.