Lossless and near-lossless image compression based on multiresolution analysis

There are applications in data compression, where quality control is of utmost importance. Certain features in the decoded signal must be exactly, or very accurately recovered, yet one would like to be as economical as possible with respect to storage and speed of computation. In this paper, we present a multi-scale data-compression algorithm within Harten’s interpolatory framework for multiresolution that gives a specific estimate of the precise error between the original and the decoded signal, when measured in the L∞L∞ and in the LpLp (p=1,2p=1,2) discrete norms.The proposed algorithm does not rely on a tensor-product strategy to compress two-dimensional signals, and it provides a priori bounds of the Peak Absolute Error (PAE), the Root Mean Square Error (RMSE) and the Peak Signal to Noise Ratio (PSNR) of the decoded image that depend on the quantization parameters. In addition, after data-compression by applying this non-separable multi-scale transformation, the user has an the exact value of the PAE, RMSE and PSNR before the decoding process takes place.We show how this technique can be used to obtain lossless and near-lossless image compression algorithms.