Method for Improved Image Reconstruction in Computed Tomography and Positron Emission Tomography, Based on Compressive Sensing with Prefiltering in the Frequency Domain

Computed tomography (CT) and positron emission tomography (PET) allow many types of diagnoses and medical analyses to be performed, as well as patient monitoring in different treatment scenarios. Therefore, they are among the most important medical imaging modalities, both in clinical applications and in scientific research. However, both methods lead to radiation exposure, associated to the X-rays, used in the CT case, and to the chemical contrast that inserts a radioactive isotope into the patient’s body, in the PET case. It is possible to reduce the amount of radiation needed to attain a specified quality in these imaging techniques by using compressive sensing (CS), which reduces the number of measurements required for signal and image reconstruction, compared to standard approaches such as filtered backprojection. In this paper, we propose and evaluate a new method for the reconstruction of CT and PET images based on CS with prefiltering in the frequency domain. We start by estimating frequency-domain measurements based on the acquired sinograms. Next, we perform a prefiltering in the frequency domain to favor the sparsity required by CS and improve the reconstruction of filtered versions of the image. Based on the reconstructed filtered images, a final composition stage leads to the complete image using the spectral information from the individual filtered versions. We compared the proposed method to the standard filtered backprojection technique, commonly used in CT and PET. The results suggest that the proposed method can lead to images with significantly higher signal-to-error ratios for a specified number of measurements, both for CT (p = 8.8324e-05) and PET (p = 4.7377e-09).