MR Image Reconstruction from Raw Data


Raw Data in
Spatial Frequency Domain
What operation must be performed to reconstruct the image?

Fourier Transform (FT) 
Reconstructed Image in
Spatial Domain
In MRI, the raw data is acquired in spatial frequency space, as shown above on the left.  Notice that most of the raw data is centered about the origin of frequency space.  Low spatial frequencies contain most of the information about the image, including gross structural features and contrast.  On the other hand, high spatial frequencies at the periphery of frequency space contain information about fine details and edges -- places in the image where the signal intensity varies abruptly from one pixel to the next.  A 2-D Fourier Transform (FT) is applied to the raw data to reconstruct the image from the spatial frequency data.  The reconstructed image is a phantom object used for testing purposes in MRI, with components of varying size, shape, and material.

Now let's look at filtering...

Filtering


 
Low Pass Filtered Raw Data
What do you expect the reconstructed image to look like?

Fourier Transform (FT) 

  
Low pass filtering attenuates high frequency data and passes low frequency data, as shown by the crude low-pass filter above left. Since the raw data is comprised mostly of low spatial frequencies, most of the original data will be preserved, and the reconstructed image will look fairly similar to the original image, just a little blurrier.  The blurring is caused by the fact that the high spatial frequencies, which contain information about edges in the image, are lost.
High Pass Filtered Raw Data
What do you expect the reconstructed image to look like?

Fourier Transform (FT) 
High pass filtering attenuates low frequencies and passes high frequencies, as shown above left.  Therefore, in the reconstructed image, most of the major features of the original image are lost; however, the edges are clearly visible.