# Image Resolution Enhancement of Highly Compressively Sensed CT/PET Signals
## 1 Introduction  
Positron emission tomography-computed tomography (better known as PET-CT or PET/CT) is a nuclear medicine procedure which fuses a positron emission tomography (PET) modality with an X-ray based computed tomography (CT), to obtain sequential images from both devices during the same time period, which are then merged into a dual diagnostic image. Therefore, functional imaging acquired by PET, which illustrates the spatial distribution of metabolic or biochemical activity in the body can be more accurately aligned or correlated with anatomic imaging achieved by CT scanning [1; 2]. The 2D and 3D image reconstruction may be rendered as a function of a joint algorithm. PET-CT has modernised medical modalities in many aspects, by adding accuracy of anatomic localisation to functional imaging, which was not available for the PET imaging. For example, many medical imaging techniques in cancer treatment, surgery planning systems, radiation treatment for cancer have been under the influence of PET-CT availability has been increasingly abandoning conventional PET devices and replacing them by PET-CT devices. The idea of combining PET with CT was proposed in the early 1990s by [PERSON] and [PERSON]. Furthermore, to inherent imagealignment, the expected profit from a PET/CT hardware fusion was to use the CT images to utilise the PET attenuation correction factors [1; 2; 3]. The very first prototype PET/CT turned out to be functional in 1998, proposed by CTI PET Systems in Knoxville, TN, USA and clinically valued at the University of Pittsburgh. The project delivered a single-slice spiral CT and a rotating ECAT ART PET (a continuously rotating PET camera) procedure [2]. Other hybrid scanners have been increasing their importance [4; 5; 6]. The spatial resolution, as well as its clarity, is a critical requirement in a number of healthcare environments, including MRI, CT, and PET where studies suffer from a lack of diagnostic data due to unusably distorted images. Medical imaging modalities are widely characterised by low spatial resolution, contrast weakness, visual noise scattering, and blurring caused by the complexity of body internal tissues, which all can cause difficulties in making a correct medical diagnosis. Several different improvements are here described and claimed to be useful for improving image quality while keeping scanning times at indeed low levels. The proposed algorithm reduces artefacts caused by highly undersampled data, even in the presence of motion distortions. The presented algorithm extends the well known Iterative Back Projection technique in several ways. It nests the Bayesian MAP estimate of the noise level, globally deformable motion analysis as well as blur kernel recognition and discrete optimisation at its core [7]. In order to be able to ensure that the presented algorithm delivers great results, it combines efficient Adaptive Tomography Reconstruction with Super-Resolution reconstruction. It yields an improved CT/PET images quality as well as improved time complexity. Moreover, enhanced high-frequency components sampling improves edge representation. The method could be directly implemented to CT/PET scanners without any hardware tweaks or changes. Thus, it is clearly shown that the developed technique can provide enhanced and sharper outputs. From obvious reasons, the sharper tissue boundaries lead to higher chances to make a proper clinical diagnosis. This modality has financial aspects that need to be considered. Therefore, whether the higher acquisition costs for CT/PET will be balanced in the long-term still needs to be confirmed. The goal of this paper was to show the potential of combined techniques for enhancing CT/PET images while maintaining short acquisition times. In accordance with high public expectations, the presented algorithm can enhance image resolution without any hardware adjustments. Besides the resolution trade-offs, this method is able to reduce motion artefacts.