期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 70, 期 -, 页码 3237-3248出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2022.3183344
关键词
Signal to noise ratio; Synchronization; Noise measurement; Image reconstruction; Signal processing algorithms; Noise level; Computational complexity; Multi-reference alignment; angular synchronization; expectation-maximization
资金
- NSF-BSF [2019752]
- BSF [2020159]
- ISF [1924/21]
- Zimin Institute for Engineering Solutions Advancing Better Lives
The proposed computational framework, Synch-EM, combines angular synchronization and expectation-maximization (EM) to learn rotation distribution and accelerate the solution to the multi-reference alignment (MRA) problem significantly in high noise levels while maintaining reconstruction quality.
The multi-reference alignment (MRA) problem entails estimating an image from multiple noisy and rotated copies of itself. If the noise level is low, one can reconstruct the image by estimating the missing rotations, aligning the images, and averaging out the noise. While accurate rotation estimation is impossible if the noise level is high, the rotations can still be approximated, and thus can provide indispensable information. In particular, learning the approximation error can be harnessed for efficient image estimation. In this paper, we propose a new computational framework, called Synch-EM, that consists of angular synchronization followed by expectation-maximization (EM). The synchronization step results in a concentrated distribution of rotations; this distribution is learned and then incorporated into the EM as a Bayesian prior. The learned distribution also dramatically reduces the search space, and thus the computational load of the EM iterations. We show by extensive numerical experiments that the proposed framework can significantly accelerate EM for MRA in high noise levels, occasionally by a few orders of magnitude, without degrading the reconstruction quality.
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