Compressed Sensing in the Presence of Speckle Noise

Speckle or multiplicative noise is a critical issue in coherence-based imaging systems, such as synthetic aperture radar and optical coherence tomography. Existence of speckle noise considerably limits the applicability of such systems by degrading their performance. On the other hand, the sophistications that arise in the study of multiplicative noise have so far impeded theoretical analysis of such imaging systems. As a result, the current acquisition technology relies on heuristic solutions, such as oversampling the signal and converting the problem into a denoising problem with multiplicative noise. This paper attempts to bridge the gap between theory and practice by providing the first theoretical analysis of such systems. To achieve this goal the log-likelihood function corresponding to measurement systems with speckle noise is characterized. Then employing compression codes to model the source structure, for the case of under-sampled measurements, a compression-based maximum likelihood recovery method is proposed. The mean squared error (MSE) performance of the proposed method is characterized and is shown to scale as O(k log n/m), suggests that if the signal class is structured (i.e., k ( )<< n), accurate recovery of a signal from under-determined measurements is still feasible, even in the presence of speckle noise. Simulation results are presented that suggest image recovery under multiplicative noise is inherently more challenging than additive noise, and that the derived theoretical results are sharp.

Automated summary

This paper provides the first theoretical analysis of coherence-based imaging systems with speckle or multiplicative noise. It characterizes the log-likelihood function and proposes a compression-based maximum likelihood recovery method. The research shows that accurate recovery of a signal is still feasible even in the presence of speckle noise and under-determined measurements.