Consider a 2-D object consisting of two triangle compartments, as shown in Figure P9.4. Suppose a solution containing a 511 KeV gamma ray emitting radionuclide with concentration f = 0.5….
Show that the imaging equation in (13.63) can be written as below
In order to produce an actual image of T1, as opposed to one that is merely T1-weighted, it is necessary to take at least two separate images and use them to compute a pixel-by-pixel estimate of T1.
(a) Show that the imaging equation in (13.63) can be written as
(b) Assume that three images f1, f2, and f3 with tip angles α1, α2, and α3, respectively, are acquired. Show that the points (fi/ tan αi, fi/ sin αi), i = 1, 2, 3, should lie on a line.
(c) Using the fact shown in part (b), find a closed-form expression for an estimate of T1 given only two images f1 and f2 with different tip angles α1 and α2.