Application of generalized wavelets: an adaptive multiresolution scheme
Journal of Computational and Applied Mathematics
ACM Transactions on Information Systems (TOIS)
An improved data structure for cumulative probability tables
Software—Practice & Experience
JPEG 2000: Image Compression Fundamentals, Standards and Practice
JPEG 2000: Image Compression Fundamentals, Standards and Practice
Stability Through Synchronization in Nonlinear Multiscale Transformations
SIAM Journal on Scientific Computing
Nonlinear Harten's multiresolution on the quincunx pyramid
Journal of Computational and Applied Mathematics
A family of stable nonlinear nonseparable multiresolution schemes in 2D
Journal of Computational and Applied Mathematics
An image multiresolution representation for lossless and lossy compression
IEEE Transactions on Image Processing
The LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS
IEEE Transactions on Image Processing
Morse description and geometric encoding of digital elevation maps
IEEE Transactions on Image Processing
Hi-index | 7.29 |
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"~ and in the L"p (p=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.