List of Principal Publications
                                        Alexander Petukhov  

BOOKS:

 Introduction to Theory of Wavelet Bases, St.Petersburg State Technical University, 1999. RUS

BOOKS EDITED:

  I.Daubechies, Ten Lectures on Wavelets (Scientific Editor of Translation into Russian),  2002.

 O.Glazunova, Russian for Mathematicians (Sientific Editor), 1997.

 1.  Approximation of discontinuous functions in the  Hausdorff   metric (Russian),
      Mat. Zametki 37 (1985), No 1, 25 - 40  (Math. Rev. 86 m:42007).

 2.  On snakes and the approximation of discontinuous functions in the Hausdorff metric
      (Russian, English summary), Analysis Mathematica 11 (1985), No 1, 55 -  73
      (Math.  Rev. 87: a:42006).

 3.  The behavior of least polynomial Hausdorff deviations from 2\pi-periodic functions
      (Russian),  Vestnik  Moskov. Univ. Ser. 1 Mat. Mekh. 1985, No 3, 11 -- 15
      (Math.  Rev. 87 i:42009).

 4.  On estimates for derivatives of trigonometric  polynomials (Russian),
      Mat.  Zametki  41  (1987),  No  4,  517 - 520 (Math. Rev. 88 h: 42001).

 5.  Approximation of functions by singular integrals in the Hausdorff metric (Russian),
     Mat. Sborn. 135(177) (1988),  No 2, 235 - 252  (Math. Rev. 89 j: 41034).

 6.  On dependence  of  properties  of  function  discontinuity points set upon the rate
      of   polynomial   Hausdorff approximation (Russian), Mat. Sborn. 136(178) (1989),
      No 7, 969 -- 988.

 7.  On dependence of properties of the  function  graphs  upon the rate of its various
      approximations  (Russian),  Izv. Akad. Nauk SSSR, 55 (1991), No 1, 159 - 183.

 8.  On the approximation of functions by convolutions in  the Hausdorff metric
     (Russian), Dokl. Russian Akad. Nauk , 327(1992), No 2, 187 - 190

 9.  On convergence of sequences of convolution operators in the  Hausdorff  metric
     (Russian),  Algebra  i  Analiz,  5 (1993), No 5, 87 - 117.

10. The space of almost periodic functions with the  Hausdorff metric (Russian),
      Mat. Sborn., 185 (1994), No 3, 69 - 92.

11. On approximation of periodic distributions in the Hausdorff metric (Russian),
     Dokl. Russian Akad. Nauk, 336 (1994), No 1, 25 - 28.

12. On polinomials of the best approximation in the Hausdorff metric (Russian)
     Zapiski semimarov POMI, 217 (1994), 130 - 143.

 13. On convergence of Fourier series of functions of the classes
      Besov --- Lizorkin --- Triebel in the Hausdorff metric (Russian),
      Mat. Zametki, 56 (1994), No 1, 63 - 70.

14. On convergence of Fourier series in the Hausdorff metric,
     Real An. Exch., 20 (1994 - 1995), No 1, 59 - 60.

15. Periodic discrete wavelets (Russian), Algebra i Analiz, 8 (1996),  No 3, 151 - 183.
     Compressed Post Script files  ENGL

16.  Periodic wavelets: Construction and Algorthms.  Program on Spline Functions and
      the Theory of Wavelets. Abstracts. Centre de Recherches Matematiques. Montreal, 1996.

17. Periodic wavelets (Russian), Mat. Sborn. 188 (1997), No 10, 69 - 94. 
      Compressed Post Script files  ENGL

18. Multiresolution analysis and wavelet decompositions of  spaces of periodic distributions
     (Russian), Dokl. Russian Akad. Nauk 356 (1997), No 2, 303 - 306.
      Compressed Post Script file  RUS

 19. Recursive filter banks and image compression, Proceedings of  the 3rd St. Petersburg
      Workshop on Simulation, June 28 - July 3, 1998,  381 - 383.

20.  Biorthogonal wavelet bases with rational masks and their applications, Trudy St.Petersburg Mat.Ob., 7(1999), 168-193.
        Compressed Post Script files RUS ,  ENGL 

21.  Trigonometric rational wavelet bases, Proceedings of the International Workshop "Self-Similar Systems",
       Dubna,  July 30 - August, 7, 1998
        Compressed Post Script files  ENGL 

22. Wavelet-based video coding using image warping and overlapped block motion compensation (joint with D.Marpe, G.Heising, and H.L.Cycon), IEE Proc.-Vision, Image and Signal Processing, 148(2001), 93-101

23. Explicit construction of framelets, Appl. and Comp. Harmonic Analysis, 11(2001), 313-327

Compressed Post Script file ENGL

24.  Approximation of distributions by convolutions in the Hausdorff metric,
       East J of Approximation Theory, 8(2002), 59-94 (See also full version in Preprint of IMI, 2000:17,Univ. of South Carolina, 37p. http://www.math.sc.edu/~imip/00papers/0017.ps}).

25. Symmetric framelets, Constructive Approximation, 19 (2003), 309-328.

26. Construction of Symmetric Orthogonal Bases of Wavelets and Tight Wavelet Frames with Integer Dilation Factor, Appl. and Comp. Harmonic Analysis, 17 (2004), 198-210. ENGL

27. Fast Implementation of Orthogonal Greedy Algorithm for tight wavelet frames, European Journal on Signal Processing, 86 (2006), 471 – 479. (invited paper)

28.  Best wavelet bases for image compression generated by rational symbols, HAIT Journal of Science and Engineering C, 4 (2007), ## 1-2, 263-271.

29. (joint with M.-J. Lai) Method of Virtual Components for Constructing Wavelet Frames,  Appl. and Comp. Harm. Anal., 22 (2007), 304-318.

30. (joint with M.-J. Lai) Method of Virtual Components in the Multivariate Setting, submitted to J. of Fourier Analysis and Its Applications, 2007.

31. (joint with I. Kozlov)   L¹ Greedy Algorithm for Sparse Solutions of

Underdetermined Linear Systems, submitted to Appl. and Comp. Harm. Anal., 2008.

32. (joint with M.-J. Lai) Newton’s Method for the Sparsest Solution

of Underdetermined Linear Systems (ready for submission).

BULLETINS OR REPORTS:      

1. (joint with G. Heising, D. Marpe, and H. L. Cycon)             Enhancement to HHI-Proposal for ITU-T H.26L, ITU-T Study Group 16/Question 15, Document Q15-H-32,  Berlin (Germany), Aug. 1999.

2. (joint with G. Heising, D. Marpe, and H. L. Cycon)   Proposal for ITU-T H.26L: A Wavelet-Based Video Coding Scheme Using  OBMC and Image Warping Prediction ITU-T Study Group 16/Q. 15, Document Q15-G-36, Monterey (USA), Feb. 1999.

OTHER (SELECTED PUBLISHED CONTRIBUTIONS TO CONFERENCES):

1. (joint with R. DeVore and R.Sharpley) Motion estimation with the redundant wavelet transform, Proc. of the 3rd Workshop on Digital and Computational Video, Clearwater Beach, Nov. 14-15, 2002.

2. Framelets with many vanishing moments, Approximation Theory X: Wavelets, Splines, and Applications, C.Chui, L.Shumaker, and J.St\"ockler (eds.), Vanderbilt Univ. Press, 2002, 425-432.

3. (joint with D. Marpe, G. Heising, and H. L. Cycon)  Video coding using a bilinear image warping motion model and wavelet-based residual coding, Proc. SPIE Conf. on Wavelet Applications in Signal and Image Processing VII, Denver, CO, July 1999, SPIE, Vol 3813, 401 - 408.

4. Trigonometric rational wavelet bases, Self-Similar Systems, Proceedings of the International Workshop  (July 30 --- August 7, 1998, Dubna, Russia, Edited by V.B. Priezzhev  and V.P. Spiridonov, 1999.

5. Recursive filter banks and image compression, Proceedings of  the 3rd St. Petersburg Workshop on Simulation, June 28 - July 3, 1998,     381 - 383.

6.  Periodic wavelets: Construction and Algorithms,    Program on Spline Functions and the Theory of Wavelets. Centre de Recherches Matematiques. Montreal, 1996.

PATENTS:

1.     (joint with I.Kozlov and V.Zheludev) Automatic Digital Film and Video Restoration, PCT/IL 2006/001011.