Reconstructions from Partial Boundary Data II

48 mins 34 secs, 44.47 MB, MP3 44100 Hz, 125.01 kbits/sec

Share this media item:

Embed this media item:

<iframe width="_width_" height="_height_" src="https://sms.cam.ac.uk/media/1159253/embed" frameborder="0" scrolling="no" allowfullscreen></iframe>

Choose size:

About this item

Available Formats

About this item

Description:	Nachman, A (Toronto) Monday 25 July 2011, 15:15-16:00

Created:

2011-07-26 13:14

Collection:

Inverse Problems

Publisher:

Isaac Newton Institute

Nachman, A

Language:

eng (English)

Credits:

Author:	Nachman, A
Director:	Steve Greenham


Abstract:	The classical inverse boundary value problem of Calderón consists in determining the conductivity inside a body from the Dirichlet-to-Neumann map. The problem is of interest in medical imaging and geophysics, where one seeks to image the conductivity of a body by making voltage and current measurements at its surface. Bukhgeim-Uhlmann and Kenig-Sjöstrand-Uhlmann have shown that (in dimensions three and higher) uniqueness in the above problem holds even if measurements are available on possibly very small subsets of the boundary. This course will explain in detail a constructive proof of these results, obtained in joint work with Brian Street. The topics I hope to cover are: 1. Review of the reconstruction method for Calderón's problem with full data. 2. New Green's functions for the Laplacian. 3. Boundedness properties of the corresponding single layer operators. 4. New solutions of the Schrödinger equation. 5. Unique solvability of the main boundary integral equation involving only the partial Cauchy data.

Abstract:

The classical inverse boundary value problem of Calderón consists in determining the conductivity inside a body from the Dirichlet-to-Neumann map. The problem is of interest in medical imaging and geophysics, where one seeks to image the conductivity of a body by making voltage and current measurements at its surface.

Bukhgeim-Uhlmann and Kenig-Sjöstrand-Uhlmann have shown that (in dimensions three and higher) uniqueness in the above problem holds even if measurements are available on possibly very small subsets of the boundary. This course will explain in detail a constructive proof of these results, obtained in joint work with Brian Street.

The topics I hope to cover are: 1. Review of the reconstruction method for Calderón's problem with full data. 2. New Green's functions for the Laplacian. 3. Boundedness properties of the corresponding single layer operators. 4. New solutions of the Schrödinger equation. 5. Unique solvability of the main boundary integral equation involving only the partial Cauchy data.

Available Formats

Format	Quality	Bitrate	Size
MPEG-4 Video	640x360	1.83 Mbits/sec	672.37 MB	View	Download
WebM	640x360	414.3 kbits/sec	147.83 MB	View	Download
Flash Video	484x272	566.97 kbits/sec	202.51 MB	View	Download
iPod Video	480x270	504.3 kbits/sec	180.19 MB	View	Download
MP3 *	44100 Hz	125.01 kbits/sec	44.47 MB	Listen	Download
Auto	(Allows browser to choose a format it supports)