Iterative tomographic image reconstruction by compressive sampling

Positron Emission Tomography (PET) and Single Photon Emission Computerized Tomography (SPECT) are essential medical imaging tools with inherent drawback of slow data acquisition process. With the knowledge that radionuclide images are sparse in transform domain, we have applied a novel concept of Compressive Sampling on them. The proposed approach aims to reconstruct images from fewer measurements, significantly reducing scan time and radiopharmaceutical doze, with benefits for patients and health care economics. The reconstruction of tomographic images is realized by compressed sensing the 2-D Fourier projections. These 2-D projections being sparse in transform domain are sensed with fewer samples in k-space and are reconstructed without loss of fidelity. These undersampled Fourier projections can then be backprojected by employing the iterative reconstruction approach for a complete 3-D volume. Our work focuses on the acquisition of 2-D SPECT/PET projections based on compressive sampling and their reconstruction using a non-linear recovery algorithm. Compressive sampling of a phantom image and PET bone scan scintigraph with radial Fourier samples are performed. The reconstructions of these images are compared to conventionally sampled images with MSE, PSNR and a new image quality measure, Structure SIMilarity (SSIM). The results show high quality image reconstruction using considerably few measurements.