Lossless compression using the Ramanujan Sums: application to hologram compression

The Ramanujan sum, introduced by S. Ramanujan, has been utilized—among other applications—for signal processing. It has recently been suggested that transforms using the Ramanujan sums may also provide the benefit of data compression. This study presents a lossless hologram-compression method that employs transforms using the Ramanujan sums. In general, lossless compression of holograms is difficult, because the statistical properties of holograms are different from natural images. We compared the compression ratios of different hologram datasets, both with and without using Ramanujan- sums-based transforms. We found that the Ramanujan periodic transform improves the compression ratio of hologram data when using data having prime number dimensions.