A18 Noise Models and Basic Image Restoration

In this activity, we attempt to reconstruct or recover an image that has been degraded by using an a priori knowledge of the degradation phenomenon.

For the degradation process, we generate noise signals with different probability distribution functions and added them to the image. In actual image capture, noise could be caused by light levels, fluctuating temperatures, atmospheric disturbances and other factors.

The noises that we generated are those that are common in image processing applications and are given by the following formulas.

To remove additive noise, we implemented the spatial filtering method.

The filters that we used are

Below is our original image and its histogram.


Adding noise to the image changes this image histogram.

Gaussian Noise

Rayleigh Noise

Erlang (Gamma) Noise

Exponential Noise

Uniform Noise

Salt and Pepper Noise




For each noise pdf, we try to reconstruct the original image using the different filters. Our goal is to recover the appearance of the original image. A way of checking this is by comparing the reconstructed image's pdf with the original pdf. The images below show the reconstructions with their pdf.

Gaussian Noise


Rayleigh Noise

Erlang (Gamma) Noise

Exponential Noise

Uniform Noise
For the first 5 noise pdfs, all four filters were successful in reconstructing the image.
We can see, however, that only Arithmetic and Contraharmonic filters work for salt and pepper noise.

Salt and Pepper Noise with Q=0


Varying Q, we can see that negative values only clean salt noise, while positive values only clean pepper noise. Q=0 cleans both but not completely.
We do the same for another image, this time one that has a broader range of grayscale values.

Original Image


After adding noise:

Gaussian Noise

Rayleigh Noise

Erlang (Gamma) Noise

Exponential Noise

Uniform Noise

Salt and Pepper Noise



After reconstruction

Gaussian Noise

Rayleigh Noise

Erlang (Gamma) Noise

Exponential Noise

Uniform Noise

Salt and Pepper Noise w Q=0


Varying Q, we get the same effect as our first image.

In this activity, I was able to do spatial filtering to remove noise from an image. I therefore give myself a grade of 10.