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1. Then that multiresolution must have an orthonormal scaling function.

2. Orthonormal expansions at baseband and passband.

3. This paper proposes an orthonormalization method which can get the same theoretical orthonormal results with the traditional Gram-Schmidt orthogonalization process for skinny (long) matrices.

4. METHODS The authors introduced orthonormal contrast transformation to avoid auto-correlation, and proposed the tests of presuppositions by likelihood ratio statistics.

5. And an orthonormal basis of the kernel feature space is constructed.

6. On the foundation of the conception of orthonormal basis in finite dimensional Euclidean space, this paper provides the theory of completely orthonormal system in infinite dimensional Euclidean space.

7. Multi-wavelet orthonormal shell expansion is performed on the contour to get several resolution levels and average value.

8. The results show that the orthonormal function method is available to study the slip flow characteristics in the triangular microchannel.

9. Complex compactly-supported orthonormal wavelets and their applications in power system.

10. Methods In this paper, the authors introduced orthonormal contrast transformation to avid auto-correlation,[sentencedict.com/orthonormal.html] and proposed the tests of presuppositions by likelihood ratio statistics.

11. Methods In this paper, the authors introduced orthonormal contrast transformation to avoid auto-correlation, and proposed the tests of presuppositions by likelihood ratio statistics.

12. We showed that in noncommutative case, orthonormal base vectors can be chosen to be unitary operators of any fix order.

13. The results show that the orthonormal function method is applicable to study the heat transfer characteristics in the triangular microchannels.

14. The aim of our work is to strengthen localized features in basis images and to impose orthonormal characteristic of Principle Component Analysis (PCA) on NMF.

15. Based on the simple prior knowledge, an approach named as multi-scale low-frequency curve analysis based on standard orthonormal wavelets is proposed.

16. A method of fabric defect detection based on deck orthonormal wavelets has been developed in paper.

17. The results show that the error in wavelet reconstruction with redundant frames is less than that with orthonormal basis.

18. A new method for construction of multiwavelet filter coefficients matrix using orthonormal expansion technique was proposed.

19. Because the calibration method directly optimizes the camera rotation angles relative to the world coordinate system, it ensures the orthonormal constraints as well as the precise solutions.

20. Starting from perfect reconstruction filter banks, the relationship between the wavelet and the filter banks is analyzed, and the construction of complex discrete orthonormal wavelet is discussed.

21. Finally the transfer function is approximated by use of the transformed orthonormal wavelet series.

22. In the image denoising algorithms, it is also a hotspot to overcome the lack of shift invariance of discrete orthonormal wavelet transform.

23. The aim of our work is to strengthen localized features in basis images and to impose orthonormal characteristic of Principle Component Analysis on NMF.

24. The bath formula of Sn-Bi alloy electroplating was improved by condition experiment and orthonormal test.

25. The random noises of systems are shown to be restrained effectively through orthonormal scaling transformation, and estimation precision is improved.

26. A novel method for the design of log-domain filters is presented which is based on the operational simulation of orthonormal ladder network.