Ghost Images in Helioseismic Holography? Toy Models in a Uniform Medium

Helioseismic holography is a powerful technique used to probe the solar interior based on estimations of the 3D wavefield. Porter--Bojarski holography, which is a well-established method used in acoustics to recover sources and scatterers in 3D, is also an estimation of the wavefield, and hence it has the potential to be applied to helioseismology. Here we present a proof of concept study, where we compare helioseismic holography and Porter--Bojarski holography under the assumption that the waves propagate in a homogeneous medium. We consider the problem of locating a point source of wave excitation inside a sphere. Under these assumptions, we find that the two imaging methods have the same capability of locating the source, with the exception that helioseismic holography suffers from "ghost images" (i.e., artificial peaks away from the source location). We conclude that Porter--Bojarski holography may improve the current method used in helioseismology.Comment: 17 pages, 8 figure

Rate Optimal Denoising of Simultaneously Sparse and Low Rank Matrices

We study minimax rates for denoising simultaneously sparse and low rank matrices in high dimensions. We show that an iterative thresholding algorithm achieves (near) optimal rates adaptively under mild conditions for a large class of loss functions. Numerical experiments on synthetic datasets also demonstrate the competitive performance of the proposed method

On The Effect of Hyperedge Weights On Hypergraph Learning

Hypergraph is a powerful representation in several computer vision, machine learning and pattern recognition problems. In the last decade, many researchers have been keen to develop different hypergraph models. In contrast, no much attention has been paid to the design of hyperedge weights. However, many studies on pairwise graphs show that the choice of edge weight can significantly influence the performances of such graph algorithms. We argue that this also applies to hypegraphs. In this paper, we empirically discuss the influence of hyperedge weight on hypegraph learning via proposing three novel hyperedge weights from the perspectives of geometry, multivariate statistical analysis and linear regression. Extensive experiments on ORL, COIL20, JAFFE, Sheffield, Scene15 and Caltech256 databases verify our hypothesis. Similar to graph learning, several representative hyperedge weighting schemes can be concluded by our experimental studies. Moreover, the experiments also demonstrate that the combinations of such weighting schemes and conventional hypergraph models can get very promising classification and clustering performances in comparison with some recent state-of-the-art algorithms