We study how to estimate a nearly low-rank Toeplitz covariance matrix T from compressed measurements. Recent work of Qiao and Pal addresses this problem by combining sparse rulers (sparse linear arrays) with frequency finding (sparse Fourier transform) algorithms applied to the Vandermonde decomposition of T . Analytical bounds on the sample complexity are shown, under the assumption of sufficiently large gaps between the frequencies in this decomposition.In this work, we introduce random ultra-sparse rulers and propose an improved approach based on these objects. Our random rulers effectively apply a random permutation to the frequencies in T 's Vandermonde decomposition, letting us avoid frequency gap assumptions and leading to improved sample complexity bounds. In the special case when T is circulant, we theoretically analyze the performance of our method when combined with sparse Fourier transform algorithms based on random hashing. We also show experimentally that our ultra-sparse rulers give significantly more robust and sample efficient estimation then baseline methods.

A deep decoder neural network is applied towards the enhancement of recent algorithms for holographic Coherent Diffraction Imaging (CDI). This method does not re- quire training data, and provides improved imaging given noisy low-photon CDI data.

We present a new technique to continuously measure and compensate the global difference coupling coefficient through the continuous measurements of eigenmode projection parameters, using a high resolution phase-locked-loop (PLL) tune meter. First, four eigenmode projection parameters are defined as the observables for weak difference coupling. Then, their analytical expressions are obtained using the strict matrix treatment and the Hamiltonian perturbation theory of linear coupling. From these parameters, the complex global coupling coefficient can be fully determined and