Multiresolution analysis on local fields

Local Multiresolution Path Planning

Grid-based methods for finding cost optimal paths are popular because of their flexibility and simple implementation. However, their computational complexity becomes unfeasible for real-time path planning if the resolution of the grid is high. These methods assume complete knowledge about the world, but in dynamic environments where sensing is done on board the robot, less is known about far-aw...

Multiresolution Random Fields and Their Application to Image Analysis

Wavelet-based multiresolution local tomography

We develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross section of a body, using almost completely local data that significantly reduces the amount of exposure and computations in X-ray tomography. The p...

Harmonic analysis on local fields and adelic spaces I

We develop a harmonic analysis on objects of some category C 2 of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. The main result is the theory of the Fourier transform on these objects and two-dimensional Poisson formulas.

Lecture Notes on Local Fields

In this case, I have corrected the Texnical errors. Also I have corrected some mathematical errors that I found – which were mercifully slight. Overall my 23 year-old mathematical self bears a closer resemblance to the current model than I might have expected (good news or bad?). If I would say something different today, I make a brief comment about it, but I have made no attempt to systematica...