Wojciech Czaja

Schroedinger Eigenmaps for the Analysis of Biomedical Data

We introduce Schroedinger Eigenmaps (SE), a new semi-supervised manifold learning and recovery technique. This method is based on an implementation of graph Schroedinger operators with appropriately constructed barrier potentials as carriers of labeled information. We use our approach for the analysis of standard biomedical datasets and new multispectral retinal images.

The Balian-Low theorem and regularity of Gabor systems

AbstractFor any positive real numbers A, B, and d satisfying the conditions

Boundedness of pseudodifferential operators on modulation spaces

\frac{1}{A} + \frac{1}{B} = 1

Schroedinger Eigenmaps with nondiagonal potentials for spatial-spectral clustering of hyperspectral imagery

, d>2, we construct a Gabor orthonormal basis for L2(ℝ), such that the generating function g∈L2(ℝ) satisfies the condition:∫ℝ|g(x)|2(1+|x|A)/logd(2+|x|)dx < ∞ and

Recent Developments in the Balian-Low Theorem

\int_{\hat {\mathbb{R}}} {\left| {\hat g(\xi )} \right|^2 (1 + \left| \xi \right|^B )/\log ^d (2 + \left| \xi \right|)d\xi< \infty }

An optimal example for the balian-low uncertainty principle

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