IEEE Proof IEEE TRANSACTIONS ON IMAGE PROCESSING 1 Novel Example-Based Method for Super-Resolution and Denoising of Medical Images Dinh-Hoan Trinh, Member, IEEE, Marie Luong, Member, IEEE, Françoise Dibos, Jean-Marie Rocchisani, Canh-Duong Pham, and Truong Q. Nguyen, Fellow, IEEE Abstract—In this paper, we propose a novel example-based method for denoising and super-resolution of medical images. The objective is to estimate a high-resolution image from a single noisy low-resolution image, with the help of a given database of high and low-resolution image patch pairs. Denoising and super-resolution in this paper is performed on each image patch. For each given input low-resolution patch, its high- resolution version is estimated based on finding a nonnegative sparse linear representation of the input patch over the low- resolution patches from the database, where the coefficients of the representation strongly depend on the similarity between the input patch and the sample patches in the database. The problem of finding the nonnegative sparse linear representation is modeled as a nonnegative quadratic programming problem. The proposed method is especially useful for the case of noise- corrupted and low-resolution image. Experimental results show that the proposed method outperforms other state-of-the-art super-resolution methods while effectively removing noise. Index Terms— Example-based super-resolution, denoising, medical imaging, sparse representation. I. I NTRODUCTION I MAGES with high resolution are desirable in many applica- tions, such as medical imaging, video surveillance, astron- omy, etc. In medical imaging, images are obtained for medical purposes, providing information about the anatomy, the phys- iologic and metabolic activities of the volume below the skin. The arrival of digital medical imaging technologies such as Computerized Tomography (CT), Positron Emission Tomog- raphy (PET), Magnetic Resonance Imaging (MRI), as well as combined modalities, e.g. SPECT/CT has revolutionized modern medicine [1], [2]. Despite the advances in acquisition Manuscript received November 16, 2013; accepted January 30, 2014. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Marios S. Pattichis. D.-H. Trinh and C.-D. Pham are with the Center for Informatics and Computing, Vietnam Academy of Science and Technology, Hanoi 10 999, Vietnam (e-mail: tdhoan@cic.vast.vn; pcduong@cic.vast.vn). M. Luong is with the Laboratoire de Traitement et Transport de l’Information, Université Paris 13, Sorbonne Paris Cité, Villetaneuse 93430, France (e-mail: marie.luong@univ-paris13.fr). F. Dibos is with the Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Sorbonne Paris Cité, Villetaneuse 93430, France (e-mail: dibos@math.univ-paris13.fr). J.-M. Rocchisani is with the University Hospitals Paris-Seine-Saint Denis, Bobigny 93066, France, and also with the Université Paris 13, Sorbonne Paris Cité, Villetaneuse 93430, France (e-mail: rocchisani@univ-paris13.fr). T. Q. Nguyen is with the Department of Electrical and Computer Engi- neering, University of California, San Diego, CA 92093 USA (e-mail: tqn001@ucsd.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIP.2014.2308422 technology and the performance of optimized reconstruction algorithms over the two last decades, it is not easy to obtain an image at a desired resolution due to imaging environments, the limitations of physical imaging systems as well as quality- limiting factors such as noise and blur. Noise which is inherent in medical imaging, may reduce adversely the contrast and the visibility of details that could contain vital information, thus compromising the accuracy and the reliability of pathological diagnosis. Enhancing spatial resolution is an alternative solution to improving resolution, i.e. to detect and discriminate the small- est possible details that can be seen, providing hence a helpful aid for better detection and diagnosis accuracy. This issue has attracted researchers with high interest for medical applications (e.g. [3] for PET images; [4], [5] for MRI; [6] for Ultrasound; [7], [8]). How to enhance spatial resolution while effectively reducing noise is still a challenging problem in medical imaging especially when the images are severely corrupted by noises. The conventional and well-known interpolation techniques [9]–[11] for enhancing image resolution are unfortunately inefficient when the given low-resolution image is corrupted by noise. Moreover, these techniques may also introduce blurring, ringing, as well as aliasing artifacts. Another technique to alleviate this problem is super-resolution (SR) which consists of generating a high-resolution (HR) image from a low- resolution (LR) image, using additional information such as multiple low-resolution (LR) images or a database that learns relationship between low and high-resolution images. A good overview of the SR methods can be found in [12]–[14]. Since the first idea was introduced by Huang and Tsai [15], many SR methods have been proposed and can be broadly categorized into two main groups: multi-image SR [15]–[18] and single-image SR [19]–[33]. In the multi-image super-resolution method, a HR image is reconstructed by exploiting information from different sub- pixel shifted LR images of the same scene. A typical solution for super-resolution from an image sequence involves three sub-tasks: registration, fusion and deblurring. The first and most important task of these methods is motion estimation or registration between LR images because the precision of the estimation is crucial for the success of the whole method [12]. However, it is difficult to accurately estimate motions between multiple blurred and noisy LR images in applications involving complex movements. This is the reason why multi-image- based SR methods is not ready for practical applications. 1057-7149 © 2014 IEEE. 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