Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Data compression by linear prediction for storage and transmission of EEG signals

The EEG time series has been subjected to various formalisms of analysis to extract meaningful information regarding the underlying neural events. In this paper the linear prediction (LP) method has been used for analysis and presentation of spectral array data for the better visualisation of background EEG activity. It has also been used for signal generation, efficient data storage and transmission of EEG. The LP method is compared with the standard Fourier method of compressed spectral array (CSA) of the multichannel EEG data. The autocorrelation autoregressive (AR) technique is used for obtaining the LP coefficients with a model order of 15. While the Fourier method reduces the data only by half, the LP method just requires the storage of signal variance and LP coefficients. The signal generated using white Gaussian noise as the input to the LP filter has a high correlation coefficient of 0.97 with that of original signal, thus making LP as a useful tool for storage and transmission of EEG. The biological significance of Fourier method and the LP method in respect to the microstructure of neuronal events in the generation of EEG is discussed.

An 8-to-1 bit 1-MS/s SAR ADC With VGA and Integrated Data Compression for Neural Recording

Low power consumption per channel and data rate minimization are two key challenges which need to be addressed in future generations of neural recording systems (NRS). Power consumption can be reduced by avoiding unnecessary processing whereas data rate is greatly decreased by sending spike time-stamps along with spike features as opposed to raw digitized data. Dynamic range in NRS can vary with time due to change in electrode-neuron distance or background noise, which demands adaptability. An analog-to-digital converter (ADC) is one of the most important blocks in a NRS. This paper presents an 8-bit SAR ADC in 0.13-mu m CMOS technology along with input and reference buffer. A novel energy efficient digital-to-analog converter switching scheme is proposed, which consumes 37% less energy than the present state-of-the-art. The use of a ping-pong input sampling scheme is emphasized for multichannel input to alleviate the bandwidth requirement of the input buffer. To reduce the data rate, the A/D process is only enabled through the in-built background noise rejection logic to ensure that the noise is not processed. The ADC resolution can be adjusted from 8 to 1 bit in 1-bit step based on the input dynamic range. The ADC consumes 8.8 mu W from 1 V supply at 1 MS/s speed. It achieves effective number of bits of 7.7 bits and FoM of 42.3 fJ/conversion-step.

Lossless data compression scheme based on neural network and SVM

First, the compression-awaited data are regarded Lis character strings which are produced by virtual information source mapping M. then the model of the virtual information source M is established by neural network and SVM. Last we construct a lossless data compression (coding) scheme based oil neural network and SVM with the model, an integer function and a SVM discriminant. The scheme differs from the old entropy coding (compressions) inwardly, and it can compress some data compressed by the old entropy coding.

Nonparametric Estimation of Data Dimensionality Prior to Data Compression: the case of the Human Development Index

In many applications in applied statistics researchers reduce the complexity of a data set by combining a group of variables into a single measure using factor analysis or an index number. We argue that such compression loses information if the data actually has high dimensionality. We advocate the use of a non-parametric estimator, commonly used in physics (the Takens estimator), to estimate the correlation dimension of the data prior to compression. The advantage of this approach over traditional linear data compression approaches is that the data does not have to be linearized. Applying our ideas to the United Nations Human Development Index we find that the four variables that are used in its construction have dimension three and the index loses information.

Arithmetic bit recycling data compression

La compression des données est la technique informatique qui vise à réduire la taille de l’information pour minimiser l’espace de stockage nécessaire et accélérer la transmission des données dans les réseaux à bande passante limitée. Plusieurs techniques de compression telles que LZ77 et ses variantes souffrent d’un problème que nous appelons la redondance causée par la multiplicité d’encodages. La multiplicité d’encodages (ME) signifie que les données sources peuvent être encodées de différentes manières. Dans son cas le plus simple, ME se produit lorsqu’une technique de compression a la possibilité, au cours du processus d’encodage, de coder un symbole de différentes manières. La technique de compression par recyclage de bits a été introduite par D. Dubé et V. Beaudoin pour minimiser la redondance causée par ME. Des variantes de recyclage de bits ont été appliquées à LZ77 et les résultats expérimentaux obtenus conduisent à une meilleure compression (une réduction d’environ 9% de la taille des fichiers qui ont été compressés par Gzip en exploitant ME). Dubé et Beaudoin ont souligné que leur technique pourrait ne pas minimiser parfaitement la redondance causée par ME, car elle est construite sur la base du codage de Huffman qui n’a pas la capacité de traiter des mots de code (codewords) de longueurs fractionnaires, c’est-à-dire qu’elle permet de générer des mots de code de longueurs intégrales. En outre, le recyclage de bits s’appuie sur le codage de Huffman (HuBR) qui impose des contraintes supplémentaires pour éviter certaines situations qui diminuent sa performance. Contrairement aux codes de Huffman, le codage arithmétique (AC) peut manipuler des mots de code de longueurs fractionnaires. De plus, durant ces dernières décennies, les codes arithmétiques ont attiré plusieurs chercheurs vu qu’ils sont plus puissants et plus souples que les codes de Huffman. Par conséquent, ce travail vise à adapter le recyclage des bits pour les codes arithmétiques afin d’améliorer l’efficacité du codage et sa flexibilité. Nous avons abordé ce problème à travers nos quatre contributions (publiées). Ces contributions sont présentées dans cette thèse et peuvent être résumées comme suit. Premièrement, nous proposons une nouvelle technique utilisée pour adapter le recyclage de bits qui s’appuie sur les codes de Huffman (HuBR) au codage arithmétique. Cette technique est nommée recyclage de bits basé sur les codes arithmétiques (ACBR). Elle décrit le cadriciel et les principes de l’adaptation du HuBR à l’ACBR. Nous présentons aussi l’analyse théorique nécessaire pour estimer la redondance qui peut être réduite à l’aide de HuBR et ACBR pour les applications qui souffrent de ME. Cette analyse démontre que ACBR réalise un recyclage parfait dans tous les cas, tandis que HuBR ne réalise de telles performances que dans des cas très spécifiques. Deuxièmement, le problème de la technique ACBR précitée, c’est qu’elle requiert des calculs à précision arbitraire. Cela nécessite des ressources illimitées (ou infinies). Afin de bénéficier de cette dernière, nous proposons une nouvelle version à précision finie. Ladite technique devienne ainsi efficace et applicable sur les ordinateurs avec les registres classiques de taille fixe et peut être facilement interfacée avec les applications qui souffrent de ME. Troisièmement, nous proposons l’utilisation de HuBR et ACBR comme un moyen pour réduire la redondance afin d’obtenir un code binaire variable à fixe. Nous avons prouvé théoriquement et expérimentalement que les deux techniques permettent d’obtenir une amélioration significative (moins de redondance). À cet égard, ACBR surpasse HuBR et fournit une classe plus étendue des sources binaires qui pouvant bénéficier d’un dictionnaire pluriellement analysable. En outre, nous montrons qu’ACBR est plus souple que HuBR dans la pratique. Quatrièmement, nous utilisons HuBR pour réduire la redondance des codes équilibrés générés par l’algorithme de Knuth. Afin de comparer les performances de HuBR et ACBR, les résultats théoriques correspondants de HuBR et d’ACBR sont présentés. Les résultats montrent que les deux techniques réalisent presque la même réduction de redondance sur les codes équilibrés générés par l’algorithme de Knuth.

An approximate dynamic programming approach for improving accuracy of lossy data compression by Bloom filters

Bloom filters are a data structure for storing data in a compressed form. They offer excellent space and time efficiency at the cost of some loss of accuracy (so-called lossy compression). This work presents a yes-no Bloom filter, which as a data structure consisting of two parts: the yes-filter which is a standard Bloom filter and the no-filter which is another Bloom filter whose purpose is to represent those objects that were recognised incorrectly by the yes-filter (that is, to recognise the false positives of the yes-filter). By querying the no-filter after an object has been recognised by the yes-filter, we get a chance of rejecting it, which improves the accuracy of data recognition in comparison with the standard Bloom filter of the same total length. A further increase in accuracy is possible if one chooses objects to include in the no-filter so that the no-filter recognises as many as possible false positives but no true positives, thus producing the most accurate yes-no Bloom filter among all yes-no Bloom filters. This paper studies how optimization techniques can be used to maximize the number of false positives recognised by the no-filter, with the constraint being that it should recognise no true positives. To achieve this aim, an Integer Linear Program (ILP) is proposed for the optimal selection of false positives. In practice the problem size is normally large leading to intractable optimal solution. Considering the similarity of the ILP with the Multidimensional Knapsack Problem, an Approximate Dynamic Programming (ADP) model is developed making use of a reduced ILP for the value function approximation. Numerical results show the ADP model works best comparing with a number of heuristics as well as the CPLEX built-in solver (B&B), and this is what can be recommended for use in yes-no Bloom filters. In a wider context of the study of lossy compression algorithms, our researchis an example showing how the arsenal of optimization methods can be applied to improving the accuracy of compressed data.

A firmware data compression unit /

Originally presented as the author's thesis (M.S.), University of Illinois at Urbana-Champaign.

Data compression for character strings /

Mode of access: Internet.

Applications of fractals to image data compression

Digital image processing is exploited in many diverse applications but the size of digital images places excessive demands on current storage and transmission technology. Image data compression is required to permit further use of digital image processing. Conventional image compression techniques based on statistical analysis have reached a saturation level so it is necessary to explore more radical methods. This thesis is concerned with novel methods, based on the use of fractals, for achieving significant compression of image data within reasonable processing time without introducing excessive distortion. Images are modelled as fractal data and this model is exploited directly by compression schemes. The validity of this is demonstrated by showing that the fractal complexity measure of fractal dimension is an excellent predictor of image compressibility. A method of fractal waveform coding is developed which has low computational demands and performs better than conventional waveform coding methods such as PCM and DPCM. Fractal techniques based on the use of space-filling curves are developed as a mechanism for hierarchical application of conventional techniques. Two particular applications are highlighted: the re-ordering of data during image scanning and the mapping of multi-dimensional data to one dimension. It is shown that there are many possible space-filling curves which may be used to scan images and that selection of an optimum curve leads to significantly improved data compression. The multi-dimensional mapping property of space-filling curves is used to speed up substantially the lookup process in vector quantisation. Iterated function systems are compared with vector quantisers and the computational complexity or iterated function system encoding is also reduced by using the efficient matching algcnithms identified for vector quantisers.