2013/05/13 by Volker Pohl, Pohl, Volker, Fanny Yang +3 · 3 citations
Computer Science · Engineering · Mathematics · #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Sparse and Compressive Sensing Techniques #cs.IT #math.IT #msc:30D10 #msc:42C15 #msc:94A12 #msc:94A20
paper · pdf · doi:10.48550/arxiv.1305.2789
Preprint accepted for publication in the Journal of Fourier Analysis and Applications
arxiv created 2014/07/10 · arxiv updated 2014/07/11
This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of their frequency samples. It proposes a sampling scheme which involves a combination of oversampling and modulations with complex exponentials. Sufficient conditions are given such that almost every signal with compact support can be reconstructed up to a unimodular constant using only its magnitude samples in the frequency domain. Finally it is shown that an average sampling rate of four times the Nyquist rate is enough to reconstruct almost every time-limited signal.