A new approach to radionuclide imaging using compressed sensing

Single-photon emission computerised tomography (SPECT) and positron emission tomography (PET) are essential medical imaging tools, with inherent drawback of slow data acquisition process. We present a novel compressed sensing-based reconstruction of these images from significantly fewer measurements than traditionally required, thus demonstrating potential of reduction in scan time and radiopharmaceutical doze with benefits for patients and health care economics. Our work effectively shows that high fidelity two-dimensional (2D) SPECT/PET image is reconstructed using compressive sensing with considerably reduced numbers of samples in acquisition stage. The reconstruction of tomographic images is realised by compressed sensing the 2D Fourier projections of k-space data. These 2D projections being sparse in transform domain need 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 three-dimensional (3D) volume. Compressed sensing of a phantom image and PET bone scintigraphy with radial Fourier samples are performed. The reconstructions of these images are compared to conventionally sampled images using image quality measures like mean square error, peak signal-to-noise ratio and structure similarity (SSIM) index, showing high-quality image reconstruction.