Software

My research has developed a number of software packages. A brief summary of some of the packages is included below, together with links to the papers and code.

• Fast expansions into harmonics: fast and provably accurate algorithms to transform between functions represented on Cartesian grids in 2D and 3D and their expansions in the eigenbasis of the Dirichlet Laplacian on the unit disk (in 2D) and unit ball in (3D). These have significantly improved complexity compared to dense methods. code, paper (2D), code, paper (3D) .

• Fast principal component analysis for Cryo-EM images: a fast method for computing the covariance matrix for cryo-EM images. Applications include fast principal component analysis and denoising. code, paper

• Subspace method of moments for ab initio 3-D single-particle Cryo-EM reconstruction: a framework for cryo-EM reconstruction with the method-of-moments using tensor sketching and low-rank decomposition. code, paper

• Tensor-ring decomposition: a number of algorithms for, and computing with, the tensor-ring decomposition to compress high-dimensional data. code, paper

• Multi-resolution tensor decompositions: a black-box compression format for high-dimensional tensors with a multiscale structure. code, paper