I.J. Image, Graphics and Signal Processing, 2017, 1, 1-9 Published Online January 2017 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijigsp.2017.01.01 Copyright © 2017 MECS I.J. Image, Graphics and Signal Processing, 2017, 1, 1-9 Super Resolution of PET Images using Hybrid Regularization Jose Mejia 1 1 UACJ/Department of electrical and computation, Juarez, Mexico Email: jose.mejia@uacj.mx.org Boris Mederos 2 , Liliana Avelar-Sosa 3 and Leticia Ortega Maynez 1 2 UACJ/Department of physics and mathematics, Juarez, Mexico 3 UACJ/Department of industrial and manufacturing engineering, Juarez, Mexico Email: {boris.mederos, liliana.avelar, lortega}@uacj.mx Abstract—Positron emission tomography images are used to diagnose, staggering, and monitoring several diseases like cancer and Alzheimer, also, this technique is used in clinical research to help to assess the therapeutic and toxic effects of drugs. However, a main drawback of this modality is the poor spatial resolution due to limiting factors such as positron range, instrumentation limits and the allowable doses of radiotracer for administration to patients. These factors also lead to low signal to noise ratios in the images. In this paper, we proposed to increment the resolution of the image and reduce noise by implementing a super resolution scheme, we proposed to use a hybrid regularization consisting of a TV term plus a Tikhonov term to solve the problem of low resolution and heavy noise. By using an anatomical driven scheme to balance between regularization terms we attain a better resolution image with preservation of small structures like lesions and reduced noise without blurring the edges of images. Experimental results and comparisons with other methods of the state-of-the-art show that our proposed scheme produces better preservation of details without adding artifacts when the resolution factor is increased. Index Terms—Super-resolution, PET, total variation. I. INTRODUCTION Positron Emission Tomography (PET) scanners provide quantitative imaging of physiological processes within the body. The analysis of these processes is helpful in diagnosing and monitoring of several diseases such as cancer, epilepsy, and many others [1][2]. For PET studies, a radiotracer is administered to a subject; since the radiotracer is a radioactive substance it emits positrons that produce a pair of photons during decay. Counts of pairs of photons are registered by the scanner to reconstruct the final image. The resulting PET images are a representation of the distribution the radiotracer in the body. PET has found major uses in clinical practice and research. However, the images produced tend to be of low signal to noise ratios (SNR) and of limited spatial resolution, the former due to several phenomena such as scattering of photons and limited photon-count availability, and the later mainly due to positron range and sensor size [27][28]. These problems in the image could affect the estimation of physiological parameters causing variations in the quantitative and qualitative accuracy of the studies using PET [3]. The problem of poor resolution in PET images has been treated by improving instrumentation of the scanner [4], however, these solutions are expensive and sometimes made for a particular scanner. Another approach is to use super-resolution (SR) techniques from signal processing. Multiframe SR consist of processing several observed low resolution images (LR) to obtain a high resolution (HR) image, these methods work under the premise that each observed LR image have subpixel shifts different from the other LR images and thus providing new information to reconstruct a HR image. There exist several works in the literature aiming to solve the problem of low resolution, we review some of the most relevant algorithms proposed in the literature. In [17] a robust approach is proposed by incorporating the use of a median estimator in order to reject outlayers in the data, this method report very good results and a low computational cost, however it lacks of a proper justification as pointed out by [22]. In [16] it is proposed a Bayesian methodology to account for the SR problem, the authors also apply a variational inference methodology to find the hyper-parameters associated with the model in addition they apply a total variation regularization term to stabilize the SR problem. The results are very promising however the time required to complete a reconstruction could be prohibitive in some applications such as PET. There exists also literature of SR applied to the enhancement of PET images, in [5] it is described the use of super resolution applied to PET images, such study is based the approach of [6], where a high resolution (HR) image is estimated through back projecting the error between several observed low resolution (LR) images and the LR version of the estimated HR image, this study demonstrated the feasibility to apply SR techniques to PET imaging. The work in [7] introduced a scheme