https://scholars.lib.ntu.edu.tw/handle/123456789/640477
Title: | Efficient Multidimensional Diracs Estimation with Linear Sample Complexity | Authors: | Pan, Hanjie THIERRY BLU Vetterli, Martin |
Keywords: | continuous-domain sparsity | Finite rate of innovation (FRI) | multidimension | point source reconstruction | Issue Date: | 1-Sep-2018 | Journal Volume: | 66 | Journal Issue: | 17 | Source: | IEEE Transactions on Signal Processing | Abstract: | Estimating Diracs in continuous two or higher dimensions is a fundamental problem in imaging. Previous approaches extended one-dimensional (1-D) methods, like the ones based on finite rate of innovation (FRI) sampling, in a separable manner, e.g., along the horizontal and vertical dimensions separately in 2-D. The separate estimation leads to a sample complexity of O(KD) for K Diracs in D dimensions, despite that the total degrees of freedom only increase linearly with respect to D. We propose a new method that enforces the continuous-domain sparsity constraints simultaneously along all dimensions, leading to a reconstruction algorithm with linear sample complexity O(K), or a gain of O(KD-1) over previous FRI-based methods. The multi-dimensional Dirac locations are subsequently determined by the intersections of hypersurfaces (e.g., curves in 2-D), which can be computed algebraically from the common roots of polynomials. We first demonstrate the performance of the new multidimensional algorithm on simulated data: multidimensional Dirac location retrieval under noisy measurements. Then, we show results on real data: radio astronomy point source reconstruction (from LOFAR telescope measurements) and the direction of arrival estimation of acoustic signals (using Pyramic microphone arrays). |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/640477 | ISSN: | 1053587X | DOI: | 10.1109/TSP.2018.2858213 |
Appears in Collections: | 電機工程學系 |
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