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Fundamentals of Deterministic Signal Processing
 
 

The field of adaptive signal processing experienced dramatic growth due to the proliferation of new and exciting applications ranging from Internet, wireless communications to multimedia and quantitative finance. Adaptive systems have become an integral part of information and telecommunications industries as a result of advances in device technology. As the range of environments that these signal processing applications are expected to work are increasing, there is now a greater need for adaptive algorithms that can operate efficiently in the presence of a wide range of environmental uncertainties and volatility with relatively low computational complexity. In this context, there exist significant practical and theoretical difficulties to adaptive signal processing, since there is usually no or little knowledge about the statistical properties of the underlying signals or systems involved. Furthermore, the classical robust methods that are resilient to such challenges are overly conservative and usually static such that they provide profoundly inferior results on the average, deeming them practically useless.

In order to provide robust adaptive methods that also perform satisfactorily in real life applications, we introduce a completely radical approach to adaptive signal processing. In this project, we aim to design adaptive methods that are mathematically guaranteed to work uniformly for all possible signals without any explicit or implicit statistical assumptions on the underlying signals or systems. In this sense, this is the first approach to build adaptive systems that can operate effectively in the presence of large degrees of environmental variability and uncertainty without sacrificing performance. This radical approach would provide the required tools in data prediction, pattern estimation, attribute derivation and adaptive data modeling to deal with the open-ended and frequently changing conditions of real life applications.

Sample publications on this topic include:

-- M. A. Donmez, S. S. Kozat, ``Steady-state MSE Analysis of Convexly Constrained Mixture Methods,'' IEEE Transactions on Signal Processing, vol. 60, iss. 6, 3314-3321, 2012.

-- S. S. Kozat, A. T. Erdogan, A. C. Singer, A. H. Sayed, ``A Transient Analysis of Affine Mixtures," IEEE Transactions on Signal Processing, vol. 59, iss. 1, 6227-6232, 2011.

-- H. Ozkan, A. Akman and S. S. Kozat, ``A Novel Training Algorithm for HMMs with Partial and Noisy Access to States,'' Signal Processing, vol. 94, pp. 490-497, January 2014.

-- S. S. Kozat, A. T. Erdogan, A. C. Singer, A. H. Sayed, ``A Transient Analysis of Affine Mixtures," IEEE Transactions on Signal Processing, vol. 59, iss. 1, 6227-6232, 2011.

-- S. S. Kozat, A. C. Singer, A. T. Erdogan, A. H. Sayed, ``Unbiased Model Combinations for Adaptive Filtering," IEEE Transactions on Signal Processing, vol. 58, pp. 4421-4427, Aug. 2010.

FIGURE: A tree based adaptive prediction method for deterministic nonlinear filtering.