Image Processing

Equation (5.62) can be written in a matrix form as

$y=Ax\left(5.63\right)$

where y is the measurement vector, x is the image vector, and A is a M × N projection matrix.

5.4.2Algebraic Reconstruction Technique

Theoretically, if the inverse matrix of the matrix A in eq. (5.63) could be obtained, then the image vector x could be calculated from the measurement vector y. In practice, to obtain high-quality images, both M and N should be at least the order of 105. Therefore, A is normally a very large matrix. Taking an image of 256 × 256 as an example, to solve eq. (5.63), the numbers of rays should be equal to or bigger than the numbers of pixels in images, so M × N ≈ 4.3 × 109. To put a matrix of such size totally inside the ...