Harmonic Analysis
Partial Differential Equations, Mathematical modelling
Electrical Impedance Imaging, Process Tomography
Magnetic Resonance EIT, MRCDI
Image Processing, Wavelet

Electrical Impedance Imaging, Process Tomography

In EIT, we try to reconstruct cross-sectional conductivity (or resistivity) images of human body. We attach electrodes on the surface of a subject to inject currents and measure induced voltages. Using these boundary current-voltage measurements, an image reconstruction algorithm can produce images of tissue conductivity values.

Magnetic Resonance EIT, MRCDI

MREIT (Magnetic Resonance Electrical Impedance Tomography)
In MREIT, we try to reconstruct cross-sectional current density and conductivity (or resistivity) images of human body with high spatial and contrast resolution. Using LF-MRCDI (Low-Frequency Magnetic Resonance Current Density Imaging) technique where we acquire MR images with external current injection through surface electrodes, we first obtain images of internal magnetic flux density distribution. This internal information transforms the ill-posed inverse problem of EIT into a well-posed one in MREIT.

Image Processing, Wavelet

PDE based imaging, Level set method, Wavelet, Fourier method.

Recent progress toward image processing is so remarkable due to developments in the speed and power of computers. Special interests in image processing are the denoising problem arising in medical imaging and surveilance video( the overnight images are seriously blurred and contaminated by large noise spikes). In medical imaging, we are interested in denosing problem in MREIT(magentic resonance electric impedance tomogrpy) where the major data( z-component of the induced magentic filed in the presence of a current) contains serious noises and artifects due to technical problems in the present MRI system. Unfortunately, the standard image smoothing techniques based on Fourier series and least squares may not work very well because these methods are basically not local and result in smearing important characteristics such as edges and boundaries. We look for PDE-based denoising techniques that seems to us quite promising because we can relate it to to physical world and count on local properties of image.