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.

翻译：研究了在有闪烁噪音的情况下从线性测量中恢复结构化信号的问题,这个问题出现在合成孔径雷达和光学一致性摄影等许多成像系统中。目前的获取技术将标本过多的信号转换成多复制性噪音的问题,然而,本文件探讨了将测量数量减少到信号环境维度以下的可能性。多复制性噪音研究中出现的精密性迄今阻碍了对这些问题的理论分析。本文旨在介绍在光斑噪音下从其下取样的测量中恢复信号的第一个理论结果。它表明,如果信号等级结构有序,信号可以有效压缩,那么人们就可以从比环境维度较少的测量中获得准确的信号估计值。我们通过模拟结果来展示我们建议的方法的有效性。