Compressive Sampling with Known Spectral Energy Density

A method to improve l1 performance of the CS (Compressive Sampling) for signals with known spectral energy density is proposed. Instead of random sampling, the proposed method selects the location of samples to follow the distribution of the spectral energy. Samples collected from three different measurement methods; the uniform sampling, random sampling, and energy equipartition sampling, are used to reconstruct a given UWB (Ultra Wide Band) signal whose spectral energy density is known. Objective performance evaluation in term of PSNR (Peak Signal to Noise Ratio) indicates that the CS reconstruction of random sampling outperform the uniform sampling, while the energy equipartition sampling outperforms both of them. These results suggest that similar performance improvement can be achieved for CS-based devices, such as the compressive SFCW (Stepped Frequency Continuous Wave) radar and the compressive VLBI (Very Large Baseline Interferometry) imaging, allowing even higher acquisition speed or better reconstruction results. Keywords—Compressive Sensing, Compressive Sampling, Equipartition of Energy, Non Uniform Sampling, SFCW, UWB, VLBI