Real World Issue: Noise

Overview

In real world situations, the equipment used to take the projections is not perfect and signals are corrupted when they enter the "evil" channel.  Up until now, we were experimenting in an ideal situation since MATLAB does not often decide to suddenly change the values of your image or projections.  In order to try and simulate what doctors and scientists have to deal with when deciding on what filter to use or how many projections to take, we must introduce noise into our experiments manually.     This addition will allow us to fully emulate tomography. 

Experiment

In order to add the noise to our images, we had to add a bit more to our MATLAB code.  We used the 'randn' function in MATLAB to create a vector of random values or intensities.  These random numbers were then added to each of our projections in order to simulate the real-world noise that results from the instruments used to take the projections.  The CODE for this can be found in the 'go.m' function.  Once again, we aim to see which filters will give us the most representative recreation of our image.

Ramp Filter	Sine Wave
Inverse Ramp	"Stretched" Sine Wave

As without the noise, we found that the best results came from the ramp filter WITH a reasonably low cutoff frequency. Also, we see again that the low pass filters lose more noise but they also lose more of our original signal which reduces the clarity and sharpness of the image while our high pass filters keep the definition of the image but also allow more noise to remain.  Another point worth making is that the stretched sine wave seems to be between the inverse ramp and ramp filter.  For future analysis, we might think about further manipulating the sine wave so that it more resembles the ramp filter but then cuts off some of the higher frequencies - this may help reduce some of the noise without removing too much of the original image.

Now that all the data has been collected and described, in our conclusion we will attempt to analyze and describe why these things happen as they do.

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