Software
(Subtitle: How to check the recovery performance of a given sensing matrix?)
(Recovery of spectrally sparse signal from partial measurement/ Figuring out frequency locations in the continuous domain from partial time sampled data, or vise versa)
- Compressed hypothesis testing: To mix or not to mix?
(Finding abnormal random variable out of normal random variable from mixed observations)
In this paper, we study the problem of determining k anomalous random variables that have different probability distributions from the rest ( n − k ) random variables. Instead of sampling each individual random variable separately as in the conventional hypothesis testing, we propose to perform hypothesis testing using mixed observations that are functions of multiple random variables. We characterize the error exponents for correctly identifying the k anomalous random variables under fixed time-invariant mixed observations, random time-varying mixed observations, and deterministic time-varying mixed observations. Our error exponent characterization is through newly introduced notions of inner conditional Chernoff information and outer conditional Chernoff information. It is demonstrated that mixed observations can strictly improve the error exponents of hypothesis testing, over separate observations of individual random variables. We further characterize the optimal sensing vector maximizing the error exponents, which lead to explicit constructions of the optimal mixed observations in special cases of hypothesis testing for Gaussian random variables. These results show that mixed observations of random variables can reduce the number of required samples in hypothesis testing applications. (CODE: message passing algorithm to find abnormal random variable out of normal random variable from mixed observation)
(Extracting exact frequency locations in the continuous domain from only partial magnitude observations in the time domain)
(Direction of Arrival (DoA) estimation with auto-sensor calibration)