Nikolaos D. Atreas

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The paper makes an attempt to introduce a new approach for detection of local singularities in signals, including one-dimensional time series and two-dimensional images. Inspired by a mode of antigen processing in the immune system, our approach is based on the rigorous mathematical methods of Discrete Tree Transform (DTT) and Singular Value Decomposition(More)
The local behavior of regular wavelet sampling expansions is quantified. The term “regular” refers to the decay properties of scaling functions φ of a given multiresolution analysis. The regularity of the sampling function corresponding to φ is proved. This regularity is used to determine small intervals of sampling points so that the sampled values of a(More)
Let φ be a function in the Wiener amalgam space W∞(L1) with a non-vanishing property in a neighborhood of the origin for its Fourier transform φ̂, τ = {τn}n∈Z be a sampling set on R and V τ φ be a closed subspace of L2(R) containing all linear combinations of τ -translates of φ. In this paper we prove that every function f ∈ V τ φ is uniquely determined by(More)
(see [9] and [10]). Throughout this work, we assume that the function satis®es the following conditions: (i) j …x†j …cons:† jB…x†j=jxj1‡"; where " 0 and jB…x†j is bounded and 1-periodic function on R. (ii) P n2Z …n† eÿin converges absolutely to a function that has no zeros on ‰ÿ ; Š. It is known that conditions (i) and (ii) imply that fK…x; n†; n 2 Zg is a(More)
Abstract. We introduce a class of sparse unimodular matrices Um of order m×m, m = 2, 3, . . . . Each matrix Um has all entries 0 except for a small number of entries 1. The construction of Um is achieved by iteration, determined by the prime factorization of a positive integer m and by new dilation operators and block matrix operators. The iteration above(More)
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