Ali Akansu

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Ali Naci Akansu (born May 6, 1958) is a Turkish-American professor of electrical & computer engineering and scientist in applied mathematics.

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He is best known for his contributions to the theory and applications of linear subspace methods including sub-band and wavelet transforms, particularly the binomial QMF [1] [2] (also known as Daubechies wavelet) and the multivariate framework to design statistically optimized filter bank (eigen filter bank). [3] [4]

Biography

Akansu received his B.S. degree from the Istanbul Technical University, Turkey, in 1980, his M.S. and PhD degrees from the Polytechnic University (now New York University), Brooklyn, New York, in 1983 and 1987, respectively, all in Electrical Engineering. Since 1987, he has been with the New Jersey Institute of Technology where he is a Professor of Electrical and Computer Engineering. He was a visiting professor at Courant Institute of Mathematical Sciences of the New York University, 2009–2010.

In 1990, he showed that the binomial quadrature mirror filter bank (binomial QMF) is identical to the Daubechies wavelet filter, and interpreted and evaluated its performance from a discrete-time signal processing perspective. [5] It was an extension of his prior work on Binomial coefficient and Hermite polynomials that he developed the Modified Hermite Transformation (MHT) in 1987. [6] [7] The magnitude square functions of Binomial-QMF filters were shown to be the unique maximally flat functions in a two-band PR-QMF design formulation. [8] [9] He organized the first wavelet conference in the United States at NJIT in April 1990, [10] and, then in 1992 [11] and 1994. [12] He published the first wavelet-related engineering book in the literature entitled Multiresolution Signal Decomposition: Transforms, Subbands and Wavelets in 1992. [13]

He made contributions in the areas of optimal filter banks, [14] [15] [16] [17] [18] [19] nonlinear phase extensions of discrete Walsh-Hadamard transform [20] and discrete Fourier transform, [21] principal component analysis of first-order autoregressive process, [22] sparse approximation, [23] digital watermarking, [24] [25] [26] [27] [28] [29] financial signal processing and quantitative finance. [30] [31] [32] [33] His publications include the books A Primer for Financial Engineering: Financial Signal Processing and Electronic Trading [34] and Financial Signal Processing and Machine Learning. [35]

Akansu was a founding director of the New Jersey Center for Multimedia Research (NJCMR), 1996–2000, and NSF Industry-University Cooperative Research Center (IUCRC) for Digital Video, 1998–2000. He was the vice president for research and development of the IDT Corporation, 2000–2001, the founding president and CEO of PixWave, Inc. (an IDT Entertainment subsidiary) that has built the technology for secure peer-to-peer video distribution over the Internet. He was an academic visitor at David Sarnoff Research Center (Sarnoff Corporation), at IBM's Thomas J. Watson Research Center, and at Marconi Electronic Systems.

He is an IEEE Fellow (since 2008) with the citation for contributions to optimal design of transforms and filter banks for communications and multimedia security. [36]

According to the Mathematics Genealogy Project, as of October 2023, Akansu had a total of 25 doctorate students. [37]

Selected works

Related Research Articles

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<span class="mw-page-title-main">Wavelet</span> Function for integral Fourier-like transform

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing.

In digital signal processing, a quadrature mirror filter is a filter whose magnitude response is the mirror image around of that of another filter. Together these filters, first introduced by Croisier et al., are known as the quadrature mirror filter pair.

<span class="mw-page-title-main">Daubechies wavelet</span> Orthogonal wavelets

The Daubechies wavelets, based on the work of Ingrid Daubechies, are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support. With each wavelet type of this class, there is a scaling function which generates an orthogonal multiresolution analysis.

<span class="mw-page-title-main">Stéphane Mallat</span> French mathematician

Stéphane Georges Mallat is a French applied mathematician, concurrently appointed as Professor at Collège de France and École normale supérieure. He made fundamental contributions to the development of wavelet theory in the late 1980s and early 1990s. He has additionally done work in applied mathematics, signal processing, music synthesis and image segmentation.

<span class="mw-page-title-main">Discrete wavelet transform</span> Transform in numerical harmonic analysis

In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information.

Stransform as a time–frequency distribution was developed in 1994 for analyzing geophysics data. In this way, the S transform is a generalization of the short-time Fourier transform (STFT), extending the continuous wavelet transform and overcoming some of its disadvantages. For one, modulation sinusoids are fixed with respect to the time axis; this localizes the scalable Gaussian window dilations and translations in S transform. Moreover, the S transform doesn't have a cross-term problem and yields a better signal clarity than Gabor transform. However, the S transform has its own disadvantages: the clarity is worse than Wigner distribution function and Cohen's class distribution function.

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<span class="mw-page-title-main">Filter bank</span> Tool for Digital Signal Processing

In signal processing, a filter bank is an array of bandpass filters that separates the input signal into multiple components, each one carrying a sub-band of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal. The process of decomposition performed by the filter bank is called analysis ; the output of analysis is referred to as a subband signal with as many subbands as there are filters in the filter bank. The reconstruction process is called synthesis, meaning reconstitution of a complete signal resulting from the filtering process.

The fast wavelet transform is a mathematical algorithm designed to turn a waveform or signal in the time domain into a sequence of coefficients based on an orthogonal basis of small finite waves, or wavelets. The transform can be easily extended to multidimensional signals, such as images, where the time domain is replaced with the space domain. This algorithm was introduced in 1989 by Stéphane Mallat.

A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most of the practically relevant discrete wavelet transforms (DWT) and the justification for the algorithm of the fast wavelet transform (FWT). It was introduced in this context in 1988/89 by Stephane Mallat and Yves Meyer and has predecessors in the microlocal analysis in the theory of differential equations and the pyramid methods of image processing as introduced in 1981/83 by Peter J. Burt, Edward H. Adelson and James L. Crowley.

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The stationary wavelet transform (SWT) is a wavelet transform algorithm designed to overcome the lack of translation-invariance of the discrete wavelet transform (DWT). Translation-invariance is achieved by removing the downsamplers and upsamplers in the DWT and upsampling the filter coefficients by a factor of in the th level of the algorithm. The SWT is an inherently redundant scheme as the output of each level of SWT contains the same number of samples as the input – so for a decomposition of N levels there is a redundancy of N in the wavelet coefficients. This algorithm is more famously known as "algorithme à trous" in French which refers to inserting zeros in the filters. It was introduced by Holschneider et al.

The complex wavelet transform (CWT) is a complex-valued extension to the standard discrete wavelet transform (DWT). It is a two-dimensional wavelet transform which provides multiresolution, sparse representation, and useful characterization of the structure of an image. Further, it purveys a high degree of shift-invariance in its magnitude, which was investigated in. However, a drawback to this transform is that it exhibits redundancy compared to a separable (DWT).

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A binomial QMF – properly an orthonormal binomial quadrature mirror filter – is an orthogonal wavelet developed in 1990.

In image processing, contourlets form a multiresolution directional tight frame designed to efficiently approximate images made of smooth regions separated by smooth boundaries. The contourlet transform has a fast implementation based on a Laplacian pyramid decomposition followed by directional filterbanks applied on each bandpass subband.

<span class="mw-page-title-main">Pyramid (image processing)</span> Type of multi-scale signal representation

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Non-separable wavelets are multi-dimensional wavelets that are not directly implemented as tensor products of wavelets on some lower-dimensional space. They have been studied since 1992. They offer a few important advantages. Notably, using non-separable filters leads to more parameters in design, and consequently better filters. The main difference, when compared to the one-dimensional wavelets, is that multi-dimensional sampling requires the use of lattices . The wavelet filters themselves can be separable or non-separable regardless of the sampling lattice. Thus, in some cases, the non-separable wavelets can be implemented in a separable fashion. Unlike separable wavelet, the non-separable wavelets are capable of detecting structures that are not only horizontal, vertical or diagonal.

References

  1. A.N. Akansu, An Efficient QMF-Wavelet Structure (Binomial-QMF Daubechies Wavelets), Proc. 1st NJIT Symposium on Wavelets, April 1990.
  2. A.N. Akansu, R.A. Haddad and H. Caglar, Perfect Reconstruction Binomial QMF-Wavelet Transform, Proc. SPIE Visual Communications and Image Processing, pp. 609–618, vol. 1360, Lausanne, Sept. 1990.
  3. H. Caglar, Y. Liu and A.N. Akansu, "Statistically Optimized PR-QMF Design," Proc. SPIE Visual Communications and Image Processing, pp. 86–94, vol. 1605, Boston, Nov. 1991.
  4. H. Caglar, Y. Liu and A.N. Akansu, "Optimal PR-QMF Design for Subband Image Coding," Journal of Visual Communication and Image Representation, Vol.4, No. 3, pp. 242-253, Sept. 1993.
  5. A.N. Akansu, R.A. Haddad and H. Caglar, The Binomial QMF-Wavelet Transform for Multiresolution Signal Decomposition, IEEE Trans. Signal Process., pp. 13–19, January 1993.
  6. A.N. Akansu, Statistical Adaptive Transform Coding of Speech Signals. Ph.D. Thesis. Polytechnic University, 1987.
  7. R.A. Haddad and A.N. Akansu, A New Orthogonal Transform for Signal Coding, IEEE Transactions on Acoustics, Speech and Signal Processing, vol.36, no.9, pp. 1404-1411, September 1988.
  8. H. Caglar and A.N. Akansu, A Generalized Parametric PR-QMF Design Technique Based on Bernstein Polynomial Approximation, IEEE Trans. Signal Process., pp. 2314–2321, July 1993.
  9. O. Herrmann, On the Approximation Problem in Nonrecursive Digital Filter Design, IEEE Trans. Circuit Theory, vol CT-18, no. 3, pp. 411–413, May 1971.
  10. 1st NJIT Symposium on Wavelets, April 1990
  11. 2nd NJIT Symposium on Wavelets, March 1992
  12. 3rd NJIT Symposium on Wavelets, March 1994
  13. Akansu, Ali N.; Haddad, Richard A. (1992), Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets, Boston, MA: Academic Press, ISBN   978-0-12-047141-6
  14. A.N. Akansu and Y. Liu, "On Signal Decomposition Techniques," Optical Engineering, vol. 30, no. 7, pp. 912–920, July 1991.
  15. R.A. Haddad and A.N. Akansu, "A Class of Fast Gaussian Binomial Filters for Speech and Image Processing," IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 39, pp. 723-727, March 1991.
  16. A.N. Akansu, "Filter Banks and Wavelets in Signal Processing: A Critical Review," Proc. SPIE Video Communications and PACS for Medical Applications (Invited Paper), pp. 330-341, vol. 1977, Berlin, Oct. 1993.
  17. M.V. Tazebay and A.N. Akansu, "Progressive Optimality in Hierarchical Filter Banks," Proc. of 1st International Conference on Image Processing (ICIP), pp. 825-829, vol. 1, Austin, Nov. 1994.
  18. A.N. Akansu, "Multiplierless 2-band perfect reconstruction quadrature mirror filter (PR-QMF) banks," US Patent (US5420891A), May 30, 1995.
  19. C.A. Gonzales and A.N. Akansu, "A Very Efficient Low-bit-rate Subband Image/Video Codec Using Shift-only PR-QMF and Zero-zone Linear Quantizers," Proc. IEEE ICASSP, vol. 4, pp. 2993-2996, April 1997.
  20. A.N. Akansu and R. Poluri, "Walsh-Like Nonlinear Phase Orthogonal Codes for Direct Sequence CDMA Communications," IEEE Trans. Signal Process., vol. 55, no. 7, pp. 3800–3806, July 2007.
  21. A.N. Akansu and H. Agirman-Tosun, "Generalized Discrete Fourier Transform: Theory and Design Methods," Proc. IEEE Sarnoff Symposium, pp. 1–7, March 2009
  22. M.U. Torun and A.N.Akansu, "An Efficient Method to Derive Explicit KLT Kernel for First-Order Autoregressive Discrete Process," IEEE Transactions on Signal Processing, vol. 61, no. 15, pp. 3944–3953, Aug. 2013.
  23. O. Yilmaz and A.N.Akansu, "Quantization of Eigen Subspace for Sparse Representation," IEEE Transactions on Signal Processing, vol. 63, no. 14, pp. 3616–3625, 15 July 2015.
  24. M. Ramkumar and A.N. Akansu, "A Robust Scheme for Oblivious Detection of Watermarks / Data Hiding in Still Images," Proc. SPIE Symposium on Voice, Video and Data Communication, vol. 3528, pp. 474-481, Boston, Nov. 1998.
  25. M. Ramkumar and A.N. Akansu, "Information Theoretic Bounds for Data Hiding in Compressed Images," Proc. IEEE 2nd Workshop on Multimedia Signal Processing, pp. 267-272, Redondo Beach, Dec. 1998.
  26. M. Ramkumar and A.N. Akansu, "On the Choice of Transforms for Data Hiding in Compressed Video," Proc. IEEE ICASSP, vol. VI, pp. 3049-3052, Phoenix, March 1999.
  27. M. Ramkumar and A.N. Akansu, "Self-Noise Suppression Schemes for Blind Image Steganography," Proc. SPIE Special Session on Image Security, vol. 3845, pp. 55-65, Boston, Sept. 1999.
  28. I.B. Ozer, M. Ramkumar and A.N. Akansu, "A New Methodology for Detection of Watermarks in Geometrically Distorted Images," Proc. IEEE ICASSP, vol. IV, pp. 1963-1966, Istanbul, June 2000.
  29. H.T. Sencar, M. Ramkumar and A.N. Akansu, "A Robust Type-III Data Hiding Technique Against Cropping and Resizing Attacks," Proc. IEEE ISCAS 2002, Scottsdale, AZ, May 2002.
  30. A.N. Akansu and M.U. Torun, "Toeplitz Approximation to Empirical Correlation Matrix of Asset Returns: A Signal Processing Perspective," IEEE Journal of Selected Topics in Signal Processing, vol. 6, no. 4, pp. 319–326, Aug. 2012.
  31. M.U. Torun, A.N. Akansu and M. Avellaneda, "Portfolio Risk in Multiple Frequencies," IEEE Signal Processing Magazine, vol. 28, no. 5, pp. 61–71, Sept. 2011.
  32. A.N. Akansu and A. Xiong, "Eigenportfolios of US Equities for the Exponential Correlation Model," Journal of Investment Strategies (Risk.net), pp. 55–77, Aug. 2020.
  33. A.N. Akansu, M. Avellaneda and A. Xiong, "Quant Investing in Cluster Portfolios," Journal of Investment Strategies (Risk.net), pp. 61–78, Dec. 2020.
  34. Akansu, Ali N.; Torun, Mustafa U. (2015), A Primer for Financial Engineering: Financial Signal Processing and Electronic Trading, Boston, MA: Academic Press, ISBN   978-0-12-801561-2
  35. Akansu, Ali N.; Kulkarni, Sanjeev R.; Malioutov, Dmitry M., Eds. (2016), Financial Signal Processing and Machine Learning, Hoboken, NJ: Wiley-IEEE Press, ISBN   978-1-118-74567-0
  36. Fellow Class of 2008 Archived 13 April 2010 at the Wayback Machine IEEE: Fellow Class of 2008
  37. http://genealogy.math.ndsu.nodak.edu/id.php?id=74955 Mathematics Genealogy Project : Ali Naci Akansu