Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

Civil infrastructure condition monitoring generates large volumes of sensor data. Huge data size impedes fast and reliable distribution of sensor data, especially for wireless sensor networks. Vibration sensor data plays an important role in many useful structural health monitoring methods. This paper presents a vibration sensor data compression technique based on the lifting scheme wavelet transform (LSWT). Real sensor data from a nine-story building as well as a steel truss bridge was used to examine the compression performance of the LSWT-based vibration sensor data compression technique. It is found that the LSWT-based vibration sensor data compression technique can achieve a very high compression ratio while retaining the basic waveform properties of original sensor data. Additionally, LSWT has a feature that supports progressive compression and thus allows for multiresolution data transmission and retrieval.

Wavelet-based vibration sensor data compression technique for civil infrastructure condition monitoring

In wireless sensor networks (WSNs), it has been observed that most abnormal events persist over a considerable period of time instead of being transient. As existing anomaly detection techniques usually operate in a point-based manner that handles each observation individually, they are unable to reliably and efficiently report such long-term anomalies appeared in an individual sensor node. Therefore, in this paper, we focus on a new technique for handling data in a segment-based manner. Considering a collection of neighbouring data segments as random variables, we determine those behaving abnormally by exploiting their spatial predictabilities and, motivated by spatial analysis, specifically investigate how to implement a prediction variance detector in a WSN. As the communication cost incurred in aggregating a covariance matrix is finally optimised using the Spearman’s rank correlation coefficient and differential compression, the proposed scheme is able to efficiently detect a wide range of long-term anomalies. In theory, comparing to the regular centralised approach, it can reduce the communication cost by approximately 80 percent. Moreover, its effectiveness is demonstrated by the numerical experiments, with a real world data set collected by the Intel Berkeley ResearchLab (IBRL).

Segment-Based Anomaly Detection with Approximated Sample Covariance Matrix in Wireless Sensor Networks

Selective medical image compression techniques for telemedical and archiving applications.

To transfer the medical image from one place to another place or to store a medical image in a particular place with secure manner has become a challenge. In order to solve those problems, the medical image is encrypting and compressing before sending or saving at a place. In this paper, a new block pixel sort algorithm has been proposed for compressing the encrypted medical image. The encrypted medical image acts as an input for this compression process. During the compression, encrypted secret image E12(;) is compressed by the pixel block sort encoding (PBSE). The image is divided into four identical blocks, similar to 2×2 matrix. The minimum occurrence pixel(s) are found out from every block and the positions of the minimum occurrence pixel(s) are found using the verdict occurrence process. The pixel positions are shortened with the help of a shortening process. The features (symbols and shortened pixel positions) are extracted from each block and the extracted features are stored in a particul...

The new block pixel sort algorithm for TVC-encrypted medical image

Lossless compression of medical images using a proposed differentiation technique is explored. This scheme is based on computing weighted differences between neighboring pixel values. The performance of the proposed approach, for the lossless compression of magnetic resonance (MR) images and ultrasonic images, is evaluated and compared with the lossless linear predictor and the lossless Joint Photographic Experts Group (JPEG) standard. The residue sequence of these techniques is coded using arithmetic coding. The proposed scheme yields compression measures, in terms of bits per pixel, that are comparable with or lower than those obtained using the linear predictor and the lossless JPEG standard, respectively, with 8-b medical images. The advantages of the differentiation technique presented here over the linear predictor are: 1) the coefficients of the differentiator are known by the encoder and the decoder, which eliminates the need to compute or encode these coefficients, and 21 the computational complexity is greatly reduced. These advantages are particularly attractive in real time processing for compressing and decompressing medical images.

Differentiation applied to lossless compression of medical images

For some classes of signals, particularly those dominated by low frequency components, such as seismic data first and higher order differences between adjacent signal samples are generally smaller compared with the signal samples. In this paper, evaluating the differencing approach for losslessly compressing several classes of seismic signals is given. Three different approaches employing derivatives are developed and applied. The performance of the techniques presented and the adaptive linear predictor are evaluated and compared for the lossless compression of different seismic signal classes. The proposed differentiator approach yields comparable residual energy compared with that obtained employing the linear predictor technique. The two main advantages of the differentiation method are: (1) the coefficients are fixed integers which do not have to be encoded; and (2) greatly reduced computational complexity, relative to the existing algorithms. These advantages are particularly attractive for real time processing. They have been confirmed experimentally by compressing different seismic signals. Sample results including the compression ratio, i.e., the ratio of the number of bits per sample without compression to those with compression using arithmetically encoded residues are also given.

Lossless compression of seismic signals using differentiation

A technique for lossless compression of seismic signals is proposed. The algorithm employed is based on the equation-error structure which approximates the signal by minimizing the error in the least square sense, as a rational function, or equivalently as an auto-regressive moving-average (ARMA) process. The algorithm is implemented in the frequency domain. The performance of the proposed technique is compared to the lossless linear predictor and the lossless differentiator methods for compressing seismic signals. The approach presented here is shown to have excellent performance and compares favorably with existing techniques.

Lossless compression of seismic signals using least square, frequency domain pole-zero modeling

An algorithm for the lossless compression of different classes of images is proposed. This approach is based on modeling the original image by a rational function which consists of poles and zeros, or equivalently an Auto-Regressive Moving-Average (ARMA) process. The equation-error structure, which approximates the image by minimizing the error in the least square sense, is used to obtain the optimal coefficients of the transfer function. This technique is implemented in the frequency domain. The performance of the proposed approach for the lossless compression of different classes of images is evaluated and compared with the lossless linear predictor. The residual sequence of these schemes is coded using arithmetic coding. The suggested approach yields compression measures, in terms of bits per pixel, lower than the lossless linear predictor for compressing 8-bit gray-scale images.

Lossless compression of images employing a linear IIR model

A technique for lossless compression of seismic signals is proposed. The algorithm employed is based on the equation-error structure, which approximates the signal by minimizing the error in the least square sense and estimates the transfer characteristic as a rational function or equivalently, as an autoregressive moving-average process. The algorithm is implemented in the frequency domain. The performance of the proposed technique is compared with the lossless linear predictor and the differentiator approaches for compressing seismic signals. The residual sequence of these schemes is coded using arithmetic coding. The suggested approach yields compression measures (in terms of bits per sample) lower than the lossless linear predictor and the differentiator for compressing different classes of seismic signals.

Y.W. Nijim

Papers

Differentiation applied to lossless compression of medical images

Lossless compression of seismic signals using differentiation

Lossless compression of seismic signals using least square, frequency domain pole-zero modeling

Lossless compression of images employing a linear IIR model

Quantitative performance evaluation of the lossless compression approach using pole-zero modeling