CUDA-accelerated HD-ODETLAP: Lossy high dimensional gridded data compression

We present High-dimensional Overdetermined Laplacian Partial Differential Equations (HD-ODETLAP), an algorithm and implementation for lossy compression of high-dimensional arrays of data. HD-ODETLAP exploits autocorrelations in the data in any dimension. It also adapts to regions in the data with varying value ranges, resulting in the maximum error being closer to the RMS error. HD-ODETLAP compresses a data array by iteratively selecting a representative set of points from the array. That set of points, efficiently coded, is the compressed dataset. The compressed dataset is uncompressed by solving an overdetermined sparse system of linear equations for an approximation to the original array. HD-ODETLAP uses NVIDIA CUDA called from MATLAB to exploit GPU parallel processing to achieve considerable speedup compared to execution on a CPU. In addition, HD-ODETLAP compresses much better than JPEG2000 and 3D-SPIHT, when fixing either the average or the maximum error. An application is to facilitate storage and transmission of voluminous datasets for better climatological and environmental analysis and prediction.