Diffraction Tomography
11/22/16
Reconstruct tissue medium from measuring scattered field
can use ultrasound, microwave, or optical imaging
Incident wave !"# = !"!
!
=
1
!
sound speed !
is unit vector in incident-wave propagation direction
i
Frequency Analysis
9/1/16
Fourier analysis represents a signal as a combination of sinusoidal components
Useful for altering/operating on/filtering a signal in the frequency domain
General real form:
!
cos + = Re !(!"!) where = 2 = !
= + = ! =
Image Processing
11/10/16
Edge detection, sharpening images
!"
! !
Spatial derivitives are the key: , 0 , !" , 0 , ! ! , 0
In practice, for an image , sampled with step sizes , , use the second-order
!"
accurate finite-difference approximation to
Image Processing
10/25/16
Discrete (sampled) images
! , ! = real number at each position ! , ! for 1 , 1
Grayscale images
Grayscale values fall between 0 1 (float) or 0 255 (integer) for 8-bit depth
display methods (the vast majority). In both
Overview
08/23/16
signal variation in some quantity (amplitude/energy/number) carrying information.
Represented as continuous 1D function or discrete (sampled) function !
information the data of interest, as defined by the user.
Discrete function