  In single-molecule super-resolution microscopy, engineered point-spread
functions (PSFs) are designed to efficiently encode new molecular properties,
such as 3D orientation, into complex spatial features captured by a camera. To
fully benefit from their optimality, algorithms must estimate multi-dimensional
parameters such as molecular position and orientation in the presence of PSF
overlap and model-experiment mismatches. Here, we present a novel joint sparse
deconvolution algorithm based on the decomposition of fluorescence images into
six basis images that characterize molecular orientation. The proposed
algorithm exploits a group-sparsity structure across these basis images and
applies a pooling strategy on corresponding spatial features for robust
simultaneous estimates of the number, brightness, 2D position, and 3D
orientation of fluorescent molecules. We demonstrate this method by imaging DNA
transiently labeled with the intercalating dye YOYO-1. Imaging the position and
orientation of each molecule reveals orientational order and disorder within
DNA with nanoscale spatial precision.
