Image Processing Reference

In-Depth Information

(Choice 6) using a permittivity of 1.2 and a minimum of 12 sources

and 120 receivers. For the prior use 3 separate prior shapes to match

the target configuration (some experimentation may be required). How

does the reconstructed image using the PDFT method compare with

the Born reconstruction? Once the prior was properly configured did

it improve the performance of the reconstructed images?

Advanced exercises

1. Use
Cepstrum2
in MATLAB to generate Born and Cepstrum recon-

structions for any target consisting of two objects (Choice 1, 3, or 5)

using a permittivity of 1.5 and a minimum of 12 sources and 120 receiv-

ers. Please discuss your observations for each Born and Cepstrum

reconstruction paying special attention to the scales. Which method

performs the best? Why do you think this is?

2. Choose any target and any valid permittivity available in
Cepstrum
.

Using your choice, calculate the 2-D value for
N
, the minimum degrees

of freedom number described in Chapter 6. Now using your scenario

choice and the associated calculated value of
N
, generate reconstruc-

tions using
Cepstrum
such that the combined choice for number of

sources and receivers satisfies the conditions for
N
,
N
2
/2,
N
2
, 2
N
2
,

4
N
2
, 8
N
2
, and 16
N
2
. Do not forget to add jitter bandwidth as needed to

overcome aliasing. For which scenario does the reconstructed image

begin to look useful? What happens to the image as you increase the

source/receiver numbers above this threshold?

3. Repeat Exercise 2 above except this time use
pdFt
in lieu of
Cep-

strum2.
Utilize the PDFT method in your reconstructions and see if

this has any effect on the performance of the reconstructions. Does

this change the minimum threshold for degrees of freedom?