A General scheme for dithering multidimensional signals, and a visual instance of encoding images with limited palettes

The core contribution of this paper is to introduce a general neat scheme based on soft vector clustering for the dithering of multidimensional signals that works in any space of arbitrary dimensionality, on arbitrary number and distribution of quantization centroids, and with a computable and controllable quantization noise. Dithering upon the digitization of one-dimensional and multi-dimensional signals disperses the quantization noise over the frequency domain which renders it less perceptible by signal processing systems including the human cognitive ones, so it has a very beneficial impact on vital domains such as communications, control, machine-learning, etc. Our extensive surveys have concluded that the published literature is missing such a neat dithering scheme. It is very desirable and insightful to visualize the behavior of our multidimensional dithering scheme; especially the dispersion of quantization noise over the frequency domain. In general, such visualization would be quite hard to achieve and perceive by the reader unless the target multidimensional signal itself is directly perceivable by humans. So, we chose to apply our multidimensional dithering scheme upon encoding true-color images – that are 3D signals – with palettes of limited sets of colors to show how it minimizes the visual distortions – esp. contouring effect – in the encoded images.