Optimal modeling for complex system design

The article begins with a brief introduction to the theory describing optimal data compression systems and their performance. A brief outline is then given of a representative algorithm that employs these lessons for optimal data compression system design. The implications of rate-distortion theory for practical data compression system design is then described, followed by a description of the tensions between theoretical optimality and system practicality and a discussion of common tools used in current algorithms to resolve these tensions. Next, the generalization of rate-distortion principles to the design of optimal collections of models is presented. The discussion focuses initially on data compression systems, but later widens to describe how rate-distortion theory principles generalize to model design for a wide variety of modeling applications. The article ends with a discussion of the performance benefits to be achieved using the multiple-model design algorithms

A Progressive Universal Noiseless Coder

The authors combine pruned tree-structured vector quantization (pruned TSVQ) with Itoh's (1987) universal noiseless coder. By combining pruned TSVQ with universal noiseless coding, they benefit from the “successive approximation” capabilities of TSVQ, thereby allowing progressive transmission of images, while retaining the ability to noiselessly encode images of unknown statistics in a provably asymptotically optimal fashion. Noiseless compression results are comparable to Ziv-Lempel and arithmetic coding for both images and finely quantized Gaussian sources

A Universal Parallel Two-Pass MDL Context Tree Compression Algorithm

Computing problems that handle large amounts of data necessitate the use of lossless data compression for efficient storage and transmission. We present a novel lossless universal data compression algorithm that uses parallel computational units to increase the throughput. The length-$N$ input sequence is partitioned into $B$ blocks. Processing each block independently of the other blocks can accelerate the computation by a factor of $B$, but degrades the compression quality. Instead, our approach is to first estimate the minimum description length (MDL) context tree source underlying the entire input, and then encode each of the $B$ blocks in parallel based on the MDL source. With this two-pass approach, the compression loss incurred by using more parallel units is insignificant. Our algorithm is work-efficient, i.e., its computational complexity is $O(N/B)$. Its redundancy is approximately $B\log(N/B)$ bits above Rissanen's lower bound on universal compression performance, with respect to any context tree source whose maximal depth is at most $\log(N/B)$. We improve the compression by using different quantizers for states of the context tree based on the number of symbols corresponding to those states. Numerical results from a prototype implementation suggest that our algorithm offers a better trade-off between compression and throughput than competing universal data compression algorithms.Comment: Accepted to Journal of Selected Topics in Signal Processing special issue on Signal Processing for Big Data (expected publication date June 2015). 10 pages double column, 6 figures, and 2 tables. arXiv admin note: substantial text overlap with arXiv:1405.6322. Version: Mar 2015: Corrected a typ

Losslees compression of RGB color images

Although much work has been done toward developing lossless algorithms for compressing image data, most techniques reported have been for two-tone or gray-scale images. It is generally accepted that a color image can be easily encoded by using a gray-scale compression technique on each of the three accounts the substantial correlations that are present between color planes. Although several lossy compression schemes that exploit such correlations have been reported in the literature, we are not aware of any such techniques for lossless compression. Because of the difference in goals, the best way of exploiting redundancies for lossy and lossless compression can be, and usually are, very different. We propose and investigate a few lossless compression schemes for RGB color images. Both prediction schemes and error modeling schemes are presented that exploit inter-frame correlations. Implementation results on a test set of images yield significant improvements

Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version