A method for principal component analysis is proposed that is sparse and robust at the same time. The sparsity delivers principal components that have loadings on a small number of variables, making them easier to interpret. The robustness makes the analysis resistant to outlying observations. The principal components correspond to directions that maximize a robust measure of the variance, with...

Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with single or finite number of random functions (much smaller than the sample size $n$). In this work, we focus on high-dimensional functional processes where $p$ comparable to, even much larger $n$. Such ubiquitous various...

Abstract Structured illumination microscopy (SIM) is one of the powerful super-resolution modalities in bioscience with advantages full-field imaging and high photon efficiency. However, artifact-free image reconstruction requires precise knowledge about parameters. The sample- environment-dependent on-the-fly experimental parameters need to be retrieved a posteriori from acquired data, posing ...