Compressive Shift Retrieval

Abstract

Abstract-The classical shift retrieval problem considers two signals in vector form that are related by a shift. The problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two signals. Inspired by compressive sensing, in this paper, we seek to estimate the shift directly from compressed signals. We show that under certain conditions, the shift can be recovered using fewer samples and less computation compared to the classical setup. Of particular interest is shift estimation from Fourier coefficients. We show that under rather mild conditions only one Fourier coefficient suffices to recover the true shift.

Introducing Intangible Cultural Heritage into the Classroom and Studies of the Practice in Regional Colleges. A Case Study in Guangxi University of Science and Technology

“…To address Problem (2), various problem reformulations have been explored. Convex formulations, such as the ℓ 1 -regularized PhaseLift method [24], often use the lifting technique and solve the problem in the n × n matrix space, resulting in high computational costs. To enhance computational efficiency, nonconvex approaches [25,26,28,29] are explored, which can be formulated as:…”

“…It has been established that the minimal sample complexity required to ensure s-sparse phase retrievability in the real case is only 2s for generic sensing vectors [23]. Several algorithms have been proposed to address the sparse phase retrieval problem [24][25][26][27][28]. These approaches have been demonstrated to effectively reconstruct the ground truth using O(s 2 log n) Gaussian measurements.…”

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“…Traditionally, the shift retrieval problem is solved by maximizing the cross-correlation between the two signals. In our work [11], we have developed a compressive variant where the measurement of the signals is undersampled. While the standard procedure to shift retrieval in this case calls for the recovery of the signal itself, e.g., using compressive sensing techniques.…”