Juan R. Romero

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In this paper we investigate Isotropic Multiresolution Analysis(IMRA), isotropic refinable functions, and wavelets. The main results are the characterization of IMRAs in terms of the Lax-Wiener Theorem, and the characterization of isotropic refinable functions in terms of the support of their Fourier transform. As an immediate consequence of these results,(More)
We analyze localized textural consistencies in high-resolution X-ray CT scans of coronary arteries to identify the appearance of diagnostically relevant changes in tissue. For the efficient and accurate processing of CT volume data, we use fast wavelet algorithms associated with three-dimensional isotropic multiresolution wavelets that implement a(More)
We extend some of the classical results of the theory of multires-olution analysis (MRA) frames to Euclidean space R d ; d > 1; and provide relevant examples. In the process, we use the theory of shift-invariant sub-spaces to bring new insights to the theory of frame multiresolution analysis. In particular, we establish an analogue of the Mallat-Meyer(More)
In this dissertation, we first study the theory of frame multiresolution analysis (FMRA) and extend some of the most significant results to d-dimensional Euclidean spaces. A main feature of this theory is the fact that it was successfully applied to narrow band signals; however, the theory does have its limitations. Some orthonormal wavelets may not be(More)
In this dissertation we first consider a problem in analog to digital (A/D) conversion. We compute the power spectra of the error arising from an A/D conversion. We then design various higher dimensional analogs of A/D schemes, and compare these schemes to a standard error diffusion scheme in digital halftoning. Secondly, we study finite frames. We classify(More)
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