Joint sparsity and frequency estimation for spectral compressive sensing

Abstract

Parameter estimation from compressively sensed signals has recently received some attention. We here also consider this problem in the context of frequency sparse signals which are encountered in many application. Existing methods perform the estimation using finite dictionaries or incorporate various interpolation techniques to estimate the continuous frequency parameters. In this paper, we show that solving the problem in a probabilistic framework instead produces an asymptotically efficient estimator which outperforms existing methods in terms of estimation accuracy while still having a low computational complexity. Moreover, the proposed algorithm is also able to make inference about the sparsity level of the measured signal. The simulation code is available online.

Frequency Estimation from Compressed Measurements of a Sinusoid in MA Colored Noise

“…Frequency estimation of a sinusoid from compressed measurements given the additive white Gaussian noise (AWGN) case has been addressed in the literature [20][21][22][23]. In [20], ML estimation by grid search optimization is proposed such that the frequency estimate is that which maximizes a cost function.…”

“…In [20], ML estimation by grid search optimization is proposed such that the frequency estimate is that which maximizes a cost function. In [21], a Newton-like algorithm is used to further refine the estimate after grid search, whereas the ML estimator in [22] requires a course-fine grid search. In [23], frequency estimation from compressed measurements is cast as a linear least squares problem.…”

“…We focus on extending the work of [24] to achieve frequency estimation from compressed sinusoids in colored noise using CCS. This approach in the compressed measurements context has the advantage of reduced computational complexity in comparison with the ML approaches of [20][21][22][23] and even with the correlation-based approaches of [5,6] since no phase unwrapping is involved, as well as the applicability to the colored noise case.…”

A novel OFDM-MIMO radar with non-equidistant subcarrier interleaving and compressed sensing

“…Thus, in this paper we sometimes use the term "frequency estimation" to refer to distance-velocity estimation. The application of CS for frequency estimation is discussed in [12]- [14].…”

Distributed Compressed Sensing off the Grid

“…China. This work was partially supported by NSFC under grant number 61171171. order selection [33], [34], which can be solved efficiently using greedy methods.…”