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Pressing the sparsity advantage via data-based decomposition

Numerous ℓ1-norm reconstruction techniques have enabled exact data reconstruction with high probability from ‘k-sparse’ data. In this work, we utilize the adaptive Gram-Schmidt technique to test the limits of compressed sensing (CS) based reconstruction using total variation. The Projection-Slice Synthetic Discriminant Function (PSDF) filter naturally lends itself to compressive sensing techniques due to the inherent dimensionality reductions of the filter generated by the projection-slice theorem, or PST. In this brief study we utilize CS for the PSDF by constructing the PSDF impulse response while iteratively reducing the AGS error terms. The truncation prioritizes the vectors with regard to the error energy levels associated with the representation of the data in the Gram- Schmidt process.