Optimal Compressed Sensing and Reconstruction of Unstructured Mesh Datasets

Exascale computing promises quantities of data too large to efficiently store and transfer across networks in order to be able to analyze and visualize the results. We investigate compressed sensing (CS) as an in situ method to reduce the size of the data as it is being generated during a large-scale simulation. CS works by sampling the data on the computational cluster within an alternative function space such as wavelet bases and then reconstructing back to the original space on visualization platforms. While much work has gone into exploring CS on structured datasets, such as image data, we investigate its usefulness for point clouds such as unstructured mesh datasets often found in finite element simulations. We sample using a technique that exhibits low coherence with tree wavelets found to be suitable for point clouds. We reconstruct using the stagewise orthogonal matching pursuit algorithm that we improved to facilitate automated use in batch jobs. We analyze the achievable compression ratios and the quality and accuracy of reconstructed results at each compression ratio. In the considered case studies, we are able to achieve compression ratios up to two orders of magnitude with reasonable reconstruction accuracy and minimal visual deterioration in the data. Our results suggest that, compared to other compression techniques, CS is attractive in cases where the compression overhead has to be minimized and where the reconstruction cost is not a significant concern.