Spectral Compressed Sensing via CANDECOMP/PARAFAC Decomposition of Incomplete Tensors
For signal processing applications requiring high-resolution frequency estimation from few samples, this work offers a new approach that avoids grid-based discretization errors.
The paper addresses line spectral estimation from limited random samples, proposing a method that uses CP decomposition of a structured tensor to achieve super-resolution without discretization errors. Simulations show competitive accuracy compared to state-of-the-art algorithms.
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.