Wall clutter mitigation and target detection using Discrete Prolate Spheroidal Sequences

2016

J Fourier Anal Appl

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Many signal processing problems-such as analysis, compression, denoising, and reconstruction-can be facilitated by expressing the signal as a linear combination of atoms from a well-chosen dictionary. In this paper, we study possible dictionaries for representing the discrete vector one obtains when collecting a finite set of uniform samples from a multiband analog signal. By analyzing the spectrum of combined time-and multiband-limiting operations in the discrete-time domain, we conclude that the information level of the sampled multiband vectors is essentially equal to the time-frequency area. For representing these vectors, we consider a dictionary formed by concatenating a collection of modulated Discrete Prolate Spheroidal Sequences (DPSS's). We study the angle between the subspaces spanned by this dictionary and an optimal dictionary, and we conclude that the multiband modulated DPSS dictionary-which is simple to construct and more flexible than the optimal dictionary in practical applications-is nearly optimal for representing multiband sample vectors. We also show that the multiband modulated DPSS dictionary not only provides a very high degree of approximation accuracy in an MSE sense for multiband sample vectors (using a number of atoms comparable to the information level), but also that it can provide high-quality approximations of all sampled sinusoids within the bands of interest.

Section: Multiband Signalsmentioning

confidence: 99%

Approximating Sampled Sinusoids and Multiband Signals Using Multiband Modulated DPSS Dictionaries

2016

J Fourier Anal Appl

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“…In the context of compressive sensing, Davenport and Wakin [9] investigated multiband modulated DPSS dictionaries for sparse recovery of sampled multiband signals, and Sejdić et al [28] applied such dictionaries for recovery of physiological signals from compressive measurements. Zhu and Wakin [29] employed such dictionaries for detecting targets behind the wall in through-the-wall radar imaging, and modulated DPSS's can also be useful for mitigating wall clutter [23].…”

Section: Applicationsmentioning

confidence: 99%

The fast Slepian transform

Karnik

Applied and Computational Harmonic Analysis

et al. 2019

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The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis -also known as the Slepian basis -this representation is often overlooked in favor of the fast Fourier transform (FFT). We show that there exist fast constructions for computing approximate projections onto the leading Slepian basis elements. The complexity of the resulting algorithms is comparable to the FFT, and scales favorably as the quality of the desired approximation is increased. In the process of bounding the complexity of these algorithms, we also establish new nonasymptotic results on the eigenvalue distribution of discrete time-frequency localization operators. We then demonstrate how these algorithms allow us to efficiently compute the solution to certain least-squares problems that arise in signal processing. We also provide simulations comparing these fast, approximate Slepian methods to exact Slepian methods as well as the traditional FFT based methods. arXiv:1611.04950v2 [math.NA]

“…The ROAST could therefore be considered for use in many of the applications involving DPSS's that were described earlier in this introduction. For example, in through-the-wall radar imaging using stepped-frequency SAR [8,9], the wall return is modeled as a sampled bandpass signal and thus the ROAST can be used to efficiently mitigate the wall return at each antenna.…”

Section: Roast Construction With a Randomized Algorithmmentioning

confidence: 99%

ROAST: Rapid Orthogonal Approximate Slepian Transform

Karnik

IEEE Trans. Signal Process.

et al. 2018

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In this paper, we provide a Rapid Orthogonal Approximate Slepian Transform (ROAST) for the discrete vector that one obtains when collecting a finite set of uniform samples from a baseband analog signal. The ROAST offers an orthogonal projection which is an approximation to the orthogonal projection onto the leading discrete prolate spheroidal sequence (DPSS) vectors (also known as Slepian basis vectors). As such, the ROAST is guaranteed to accurately and compactly represent not only oversampled bandlimited signals but also the leading DPSS vectors themselves. Moreover, the subspace angle between the ROAST subspace and the corresponding DPSS subspace can be made arbitrarily small. The complexity of computing the representation of a signal using the ROAST is comparable to the FFT, which is much less than the complexity of using the DPSS basis vectors. We also give non-asymptotic results to guarantee that the proposed basis not only provides a very high degree of approximation accuracy in a mean squared error sense for bandlimited sample vectors, but also that it can provide high-quality approximations of all sampled sinusoids within the band of interest. Z. Zhu is with the Center for