Due to many occurrences in the natural environment, it becomes necessary to restore an image that was taking poorly or degraded due to noise in transmission. Not only is it possible to properly view a noisy picture, but it also possible through Digital Signal Processing Techniques to restore a picture that is blurry, and or out-of-focus.

INTRODUCTION

In this project we used MATLAB to handle all of our signal processing. All of our test images were either grayscale or converted to grayscale, as a result of the way in which matlab stores images. This is our basic model for a distorted image:

G = F * H + N.

• F is the FFT2 of the image matrix.
  
• H is the FFT2 of the complex distoring function.
  
• N is the FFT2 of the additive Gaussian Noise.
  
• G is the FFT2 of the "observed" image

INVERSE FILTERING

One of our methods for restoring images was the use of inverse filtering. In the absence of noise the equation becomes G = F * H. Thus you can see that F = G/H. Thus given G, we can reproduce F, if we can model the distortion filter accurately enough. However this is the absolute absence of noise, because other wise inverse filtering results in (F + N)/H. Inverse filtering the noise, is generally considered to be bad.

WIENER FITLERING

The wiener filtering method has the advantage over inverse filtering in that it can work on noisy distorted images. It has the form:

          |H^2|        

 Wf = ----------------


       H *|H^2| + K

• H is the FFT of the model of the distorting function.
• K is a scalar constant.

MEDIAN & MEAN FILTERING

• Inverse and Psuedoinverse Filtering
• Wiener Filtering
• Defocused Images