Efficient Image Processing Through Compressive Sampling: Bridging the Gap between Data Compression and High-Quality Reconstruction

One of the longstanding problems in digital imaging is the compression of images with sufficient fidelity for reconstruction. Common file formats like JPEG and PNG are not well suited for higher compression, so there has been a growing interest in compressive sampling as an alternative. In this paper, the basic principles of compressive sampling are appraised, and its performance is compared with traditional methods of compression on a set of 129 animal images. The compression ratios of the Sparse Transform method on the test dataset were within the range of 9.26–93.44 (mean 45.02). Mean reconstruction error was 24.14, PSNR ranged from 18.98 to 27.07 dB (mean 23.27 dB), and SSIM from 0.68 to 0.96 (mean 0.85). The results presented here indicate that, among the compressive sampling variants tested, the Sparse Transform approach rose as the best combination of compression and reconstruction quality, whereas the conventional methods (including JPEG) have better reconstruction fidelity at each operating point. Finally, the paper raises a number of questions that need to be addressed in order to continue work in this area, particularly the applicability of the method to other more specialized imaging tasks.