2021/07/31 by Wenda Zhou, Zhou, Wenda, Shirin Jalali +3 · 1 citation
Engineering · #Electrical and Bioimpedance Tomography #FOS: Computer and information sciences #Information Theory (cs.IT) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2108.00329
openalex publication_date 2021/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The current acquisition technology oversamples signals and converts the problem into a denoising problem with multiplicative noise. However, this paper explores the possibility of reducing the number of measurements below the ambient dimension of the signal. The sophistications that appear in the study of multiplicative noises have so far impeded theoretical analysis of such problems. This paper aims to present the first theoretical result regarding the recovery of signals from their undersampled measurements under the speckle noise. It is shown that if the signal class is structured, in the sense that the signals can be compressed efficiently, then one can obtain accurate estimates of the signal from fewer measurements than the ambient dimension. We demonstrate the effectiveness of the methods we propose through simulation results.