5 research outputs found
Poisson Matrix Completion
We extend the theory of matrix completion to the case where we make Poisson
observations for a subset of entries of a low-rank matrix. We consider the
(now) usual matrix recovery formulation through maximum likelihood with proper
constraints on the matrix , and establish theoretical upper and lower bounds
on the recovery error. Our bounds are nearly optimal up to a factor on the
order of . These bounds are obtained by adapting
the arguments used for one-bit matrix completion \cite{davenport20121}
(although these two problems are different in nature) and the adaptation
requires new techniques exploiting properties of the Poisson likelihood
function and tackling the difficulties posed by the locally sub-Gaussian
characteristic of the Poisson distribution. Our results highlight a few
important distinctions of Poisson matrix completion compared to the prior work
in matrix completion including having to impose a minimum signal-to-noise
requirement on each observed entry. We also develop an efficient iterative
algorithm and demonstrate its good performance in recovering solar flare
images.Comment: Submitted to IEEE for publicatio
Denoising time-resolved microscopy image sequences with singular value thresholding.
Time-resolved imaging in microscopy is important for the direct observation of a range of dynamic processes in both the physical and life sciences. However, the image sequences are often corrupted by noise, either as a result of high frame rates or a need to limit the radiation dose received by the sample. Here we exploit both spatial and temporal correlations using low-rank matrix recovery methods to denoise microscopy image sequences. We also make use of an unbiased risk estimator to address the issue of how much thresholding to apply in a robust and automated manner. The performance of the technique is demonstrated using simulated image sequences, as well as experimental scanning transmission electron microscopy data, where surface adatom motion and nanoparticle structural dynamics are recovered at rates of up to 32 frames per second.Junior Research Fellowship from Clare CollegeThis is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.ultramic.2016.05.00