Reconstrucción conjunta de imágenes de resonancia magnética e imágenes por emisión de positrones : reconstrucción conjunta de imágenes de resonancia magnética y de tomografía por emisión de positrones usando datos sintéticos.

Abstract

Often, the only way to measure a physical phenomenon is indirectly through a variable other than the one of interest. If, in addition, the measurements result from a finite sampling and we intend to determine a continuous variable, then we are faced with an indirect measurement problem. Its mathematical formulation corresponds to what is called linear inverse problems, and its solution requires tools such as variational calculus and numerical optimization. An example is medical image reconstruction, which originated in X-ray computed tomography and has evolved by taking advantage of different physical phenomena over the last half-century. For instance, today, scanners are capable of simultaneously performing both positron emission tomography (PET) and magnetic resonance imaging (MRI). The random behavior in PET determines that its images are poorly defined, while MRI images enjoy excellent reconstructions. The structural similarity of both medical imaging modalities helps the reconstructions to benefit from each other. To do this, we will use a statistical model of joint maximum a posteriori (JMAP) estimation that takes advantage of known a priori regularizers and whose solution is approximated with the L-BFGS-B Algorithm. This work presents the theoretical framework, mathematical tools, and computational implementation necessary for the joint PET/MRI reconstruction of synthetic data simulated from computer-generated test images called phamtons.