From Event: SPIE Optical Engineering + Applications, 2017
In our recent theoretical work, we have provided a complete 1-D theory for restoring signals with finite rate of innovations (FRI) from sparse Fourier measurements using low-rank Fourier interpolation. In this work, we are expanding this theory for restoring common sparse signals where the singularity of the FRI signals is at the same position, while the unknown weights are different for each channel. We consider two situations: one for the same Fourier sampling pattern, which corresponds to the multiple measurement vector problems (MMV), and the other for different sampling patterns.
We will derive performance guarantees: one for the algebraic guraantee and the other for probabilistic guarantee from randomly sampled Fourier measurements. We will discuss the relationship between the newly derived bounds and those of multiple signal classification (MUSIC) algorithm and single channel low-rank Fourier interpolation.
Jong Chul Ye, "Learning-based low-rank Hankel structured matrix approach (Conference Presentation)," Proc. SPIE 10394, Wavelets and Sparsity XVII, 103941J (Presented at SPIE Optical Engineering + Applications: August 09, 2017; Published: 26 September 2017); https://doi.org/10.1117/12.2275574.5589088587001.
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