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 Compressive Sensing (CS) as a way to reduce the size of the data as it is being stored. 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 data sets, such as image data, we investigate its usefulness for point clouds such as unstructured mesh datasets found in many finite element simulations. We sample using second generation wavelets (SGW) and reconstruct using the Stagewise Orthogonal Matching Pursuit (StOMP) algorithm. We analyze the compression ratios achievable and quality of reconstructed results at each compression rate. We are able to achieve compression ratios between 10 and 30 on moderate size datasets with minimal visual deterioration as a result of the lossy compression.