1. Advanced deconvolution techniques and medical radiography
Adrian Leslie Jannetta
Ph. D. Dissertation in 2005

2. Measure of Image Quality
MTF(Modulation Transfer Function) and Spatial Resolution
Point Spread Function

3. Signal to Noise Ratio
For a pair of image
For a single image

4. Contrast resolution and windowing
Contrast resolution: ability of an image to discern the contrast difference
ex. 8bits fir 256 levels of contrast difference
Windowing techniques for data with 1024 levels to display 256 levels 1
window

5. Contrast, signal and noise
Contrast to noise ratio

6. Image Restoration
Difference between image enhancement and image restoration
Enhancement:
does not retrieve any new information from an image but makes detail already in an image easier to see.
Restoration
Undo the degradation process, which involves the form of missing data, blurring, noise or combinations ofthose effects.

7. Types of deconvolution methods
Image formation model
Types of deconvolution methods
Algebraic deconvolution
Inverse or pseudo-inverse filtering
Wiener filtering
Regularized deconvolution
Other method

8. Algebraic deconvolution

9. Matrix representation of PSF
Sparse Block-Circulant matrix A

10. Singular Value Decomposition

15. Generalized inverse for huge matrix is necessary even though there are several fast algorithms.

16. Inverse and pseudoinverse filtering

20. Wiener Filtering Adjustable parameter is chosen by
the user to balance sharpness against noise in the restored image.

22. Regularized Deconvolution
From the original to degraded image is many to one mapping so that estimation problem from observed image is ill-posed.
Need constraint to choose an estimate from many alternatives
Can be formulated by Bayesian estimation of latent true image from observed image with prior information
Minimize the objective function with Lagrange multiplier

23. Constrained Least Square
Tendency to fit the data too strongly in least mean squared error
Noisy observed data is appeared in the estimate
Apply the smoothness constraint
Minimize the Laplacian values of image

24. Iterative Deconvolution
Basic Algorithm
Assume that PSF of degradation is known
Iterate
Problem
Not robust when applied noisy image
Hard to control the algorithm to converge

25. RL(Richardson-Lucy) deconvolution
Although RL decon-volution converges to the mathematically correct solution, a better quality restoration is usually arrived at before the method converges.
RL deconvolution has a tendency to overfit the restored image to the data (and therefore, the noise).

27. Bayesian Approach for Image Restoration

29. MAP is 1/20, but the probability [0,1/10] is 0.1.
MAP is Ok but rarely happens.
The expected value is ½.

31. Restoration is an ill-posed Problem
Ill posed problem if, under appropriate conditions, the solution fails to satisfy one or more of the following statements:
The solution exists
The solution is unique
The solution is stable
If the noise is involved, restoration problem is many to one mapping even though the degradation process is known.
It can be modelled by Bayesian network. 𝑥 𝑛 𝑑 𝑁

32. Maximum Entropy Deconvolution
An image solution is sought which has the least uncertain structure of all the solutions that are consistent with the measured data, equivalently to choosing the image having maximum entropy.

34. Hybrid Maximum Entropy Method with Intrinsic Correlation Function
Images restored by Historic MEM tend to be grainy in appearance at the very finest scales: there can often be very little correlation between neighboring pixels within the image, because pixel correlations are not be introduced into the restored image.
Allow pixel correlations in the restored image.
Hybrid Maximum Entropy Method with Intrinsic Correlation Function

39. Jos´e M. Bioucas-Dias, M´ario A. T. Figueiredo, and Jo˜ao P. Oliveira
TOTAL VARIATION-BASED IMAGE DECONVOLUTION: A MAJORIZATION-MINIMIZATION APPROACH
Jos´e M. Bioucas-Dias, M´ario A. T. Figueiredo, and Jo˜ao P. Oliveira