| Paper ID | SPTM-18.2 |
| Paper Title |
SUB-NYQUIST MULTICHANNEL BLIND DECONVOLUTION |
| Authors |
Satish Mulleti, Weizmann Institute of Science, Israel; Kiryung Lee, The Ohio State University, United States; Yonina C. Eldar, Weizmann Institute of Science, Israel |
| Session | SPTM-18: Sampling Theory, Analysis and Methods |
| Location | Gather.Town |
| Session Time: | Thursday, 10 June, 15:30 - 16:15 |
| Presentation Time: | Thursday, 10 June, 15:30 - 16:15 |
| Presentation |
Poster
|
| Topic |
Signal Processing Theory and Methods: [SMDSP] Sampling, Multirate Signal Processing and Digital Signal Processing |
| IEEE Xplore Open Preview |
Click here to view in IEEE Xplore |
| Virtual Presentation |
Click here to watch in the Virtual Conference |
| Abstract |
We consider a continuous-time sparse multichannel blind deconvolution problem. The signal at each channel is expressed as the convolution of a common source signal and its impulse response given as a sparse filter. The objective is to identify these sparse filters from sub-Nyquist samples of channel outputs by leveraging the correlation across channels. We present necessary and sufficient conditions for the unique identification. In particular, the sparse filters should not share a common sparse convolution factor and it is necessary to have 2L or more samples per channel from at least two distinct channels. We also show that L-sparse filters are uniquely identifiable from two channels provided that there are 2L^2 Fourier measurements per channel, which can be computed from sub-Nyquist samples. Additionally, in the asymptotic of the number of channels, 2L Fourier measurements per channel are sufficient. The results are applicable to the design of multi-receiver, low-rate, sensors in applications such as radar, sonar, ultrasound, and seismic exploration. |
