Image Restoration and reconstruction

Image Restoration and Reconstruction

1. Image enhancement is subjective and image restoration is objective.
2. Goal is to improve the image in some predefined sense.
3. Attempt to recover a degraded image by using  the knowledge of the degradation phenomenon which is usually available before hand.
4. Understanding the degradation process and then modeling it is the key to success here.
5. Example : Given y[m, n] and we are able to model y[m, n] = x[m, n] +η(m, n) where η = noise. We can get x[m, n] if we are able to understand η which is noise and which had degraded the original x[m, n]. By performing the inverse process of degradation on  y[m, n]  the original    x[m, n] can be restored.
6. In reality, one can only estimate η. The quality of restoration largely depends on the closeness of the estimate to η.
7. As in image enhancement, image restoration techniques are best formulated in the spatial domain, while others are better suited for the frequency domain.
8. Rule of thumb : If the noise is additive use spatial domain technique and if the degradation is a motion induced blur,  use frequency domain techniques.
9. However, additive noise is also taken care of in the frequency domain.
10. Image restoration is divided into subtopics as follows :

a.       A model of the image degradation/restoration process

b.       Understanding how to model noise

c.       Understand the PDF of some important noise distribution such as Gaussian, Rayleigh, Erlang(gamma), Exponential, Uniform, Impulse(salt-and-pepper)  noise and finally periodic noise.

11. The process of image restoration is given below

12. Noise gets added to an image at the time of image acquisition and/or transmission.
13. Factors include environmental conditions, quality of sensing elements, light levels, sensor temperature during acquisition.
14. Interference in the channel, corruption due to lightning or other atmospheric disturbance during transmission.
15. Noise models : Can be undertood through the corresponding Probability Density Function (PDF). Some of the most common and important noise PDFs are for the following : Gaussian noise, Rayleigh noise, Erlang(gamma) noise, Exponential noise, Uniform noise, Impulse (salt-and-pepper noise).
16. The above PDFs, as a group, provide useful tools for modeling a broad range of noise corruption  situations found in practice.
17. Gaussian noise is due to electronic circuit noise and sensor noise due to poor illumination and/or high temperature.
18. Rayleigh noise  density is helpful in range imaging.
19. Exponential and gamma densities find application in laser imaging.
20. Impulse  noise is found in situations where quick transients, such as faulty switching, take place during imaging.
21. An important observation is that it is difficult to differentiate visually between the first five noisy images even though their histograms are significantly different.
22. The salt-and-pepper appearance of the image corrupted by impulse noise is the only one that is visually indicative of the type of noise causing the degradation.
23. Periodic noise in an image arises typically from electrical or electromechanical interference during image acquisition. This is a spatially dependent noise which can be reduced significantly via frequency domain filtering.
24. Restoration in the presence of noise is possible through spatial filtering.
25. Spatial filters are of three types

a.      Mean filters :  Arithmetic Mean filter, Geometric Man Filter, Harmonic Mean Filter, Contraharmonic mean Filter

b.      Order-Statistic Filters : Median Filter, Max filter, Min filter, Midpoint Filter, Alpha-trimmed mean filter.

c.       Adaptive Filters : Adaptive local noise reduction filter,  Adaptive Median Filter

26. Periodic noise reduction using Frequency domain filtering : These include Bandreject filters, Bandpass filters, Notch filters, Optimum notch filters.
27. Estimating the Degradation function is done as follows :

a.       Estimation  by image observation

b.       Estimation by Experimentation.

c.       Estimation by modeling

28. Inverse Filtering in general has poor performance and is improved by the following three methods :

a.       Minimum Mean Square Error (Wiener) Filtering makes provision for the degradation function and statistical characteristics of noise into the restoration process. Here, images and noise are considered as random variables and the objective is to minimise the mean square error

b.       Constrained Least Squares Filtering

c.       Geometric Mean Filter