Garnier, Bilbro, Snyder, and Gault, "Noise Removal from MultipleMRI Images", Journal of Digital Imaging, Vol. 7, No 4, November,1994.
Garnier, Bilbro, Gault, Snyder, "Magnetic Resonance Image Restoration", Journal of Mathematical Imaging
In this project, optimization methods were applied to a vector of three measurements taken on the same brain, using MRI, in order to estimate the physical constants:
PD (proton density)
T1 (relaxation time 1)
T2 (relaxation time 2)
In the process of performing this optimzation, the image was estimated using knowledge of the statistics of the noise process, of the physics of image creation, and of the a-priori characteristics of the tissues and tissue boundaries. This allowed estimation of the characteristic parameters, after the noise had been removed, but removed without blurring of the image.The results are shown below: (You may click on one of these little images and see a larger version.
This illustrates a very noisy MRI image. The noise is so high in this case because the slice was very thin.
The same image, after processing using the optimzation algorithm.