Stochastic 2-microlocal analysis

Microlocal Analysis in Tomography

In this chapter, we introduce a range of tomography problems, including Xray imaging, limited data problems, electron microscopy and radar imaging. We are interested in the recovery of the singular features of the medium or object rather than exact inversion formulas. Toward this end, we show how microlocal analysis helps researchers understand the strengths and limitations inherent in the reco...

Introduction to Microlocal Analysis

Bay Area Microlocal Analysis Seminar

Probabilistic Weyl laws for quantized tori MACIEJ ZWORSKI UC Berkeley Abstract For the Toeplitz quantization of complex-valued functions on a 2n-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for “false” eigenvalues created by pseudospec...

An Introduction to Microlocal Analysis

Microlocal Analysis of the Geometric Separation Problem

Image data are often composed of two or more geometrically distinct constituents; in galaxy catalogs, for instance, one sees a mixture of pointlike structures (galaxy superclusters) and curvelike structures (filaments). It would be ideal to process a single image and extract two geometrically ‘pure’ images, each one containing features from only one of the two geometric constituents. This seems...