終わりだ (Activity # 19)

Activity # 19 - Restoration of Blurred Images.. this is the last of the AP 186 activities which means this sem is finally over.. well, not quite but at least it's almost done. xD

In this activity, our objective would be to restore an image corrupted by a blurring function and some noise. This entire activity can be summarized in the form of a flowchart:

In simple terms, just as the objective states, we start by taking an image, then we give it a blur by introducing a blurring function and adding a noise in the Fourier domain, and then finally restoring it using a Minimum Square Error Filter.

Since the equation for a blurred image with T as the length of exposure is defined by the equation:

for adding a blur, the degradation function would then be expressed as (also in terms of T):

As for the noise, we make use of the Gaussian Noise that was already discussed in the previous activity. The operations are performed in the Fourier domain and is described by the following equation:

The filter used for the activity is the Weiner Filter or the minimum mean square error filter given by either this

or this

where K is a constant (alternative when Sn and Sf are unknown).

So that's practically all the physics you'll ever need for the activity--what we need to do now is apply those equations to a test image. For this activity, the I grabbed a photo of Eric Clapton with 'The Fool' guitar from Gibson's site:

The blurred image generated by the degradation function looks like this:

Now, since there are two equations for the filter, we therefore have two reconstructions for the image: one using Sn and Sf (Left) and another one using K=0.01 (Right).

We can see that we have a better image using the Sn and Sf reconstruction. However, we can observe the following trend for various K's (K=1, K=0.1, K=0.01 and K=0.001 respectively:

From the set, we can infer that K approaching integer values is biased towards the blur, while small values of K are biased towards the noise. On a side note, the optimal value is hence in between K=0.1 and K=0.001.

This activity was rather easy compared to the other activities, so I'll give myself a 10. I'd like to acknowledge Neil for his help in this activity.