Abstract—In cardiac diffusion tensor magnetic resonance imaging (DT-MRI), low signal-to-noise ratio (SNR) inherently hampers the measurement accuracy of myocardium fiber structures. This paper presents a new method for filtering diffusion weighted (DW) images in cardiac DT-MRI. The method is based on sparse representation through using basis pursuit denoising (BPDN) algorithm allowing seeking overall sparest solution. It decomposes useful structures in DW images into sparsely representing atoms with Heaviside dictionary, while yielding nonsparse representation on noise, which leads to the separation of the noise from the image’s useful structures. The proposed method is evaluated on both simulated and real cardiac DW images. I. INTRODUCTION iffusion tensor magnetic resonance imaging (DT-MRI) provides the only means for in vivo and nondestructive fiber characterization of organizational and architectural feature of the brain white matter [1]-[3], myocardium[4], [5]. For instance, detailed information of three-dimensional (3D) fiber structures of myocardium is critically important to the understanding of the properties in health and disease hearts. Fiber orientation is known to be altered in various cardiac diseases such as myocardial infarction [6], ischemic heart disease and ventricular hypertrophy. However, cardiac DT-MRI is subject to noise [7]. The harmful impacts include errors in the estimation and sorting of diffusion tensors and the derived parameters such as eigenvectors, anisotropy indices, fiber orientations, etc. All that could be further aggravated by artifacts such as partial volume effects and motions during acquisition [8]. Therefore, improving the SNR is of vital importance in enhancing the practical utility of cardiac DT-MRI. Noise removal techniques are an efficient way to improve the SNR of cardiac DT-MRI without requiring additional acquisitions. Meanwhile, recently, in the field of signal and image processing, sparse representation has appeared as a promising approach for many application problems such as compression, decomposition, segmentation, regularization, denoising, etc. In particular, basis pursuit denoising (BPDN) algorithm, which is based on the well-known basis pursuit, Manuscript received March 31, 2007. Lijun Bao is both with CREATIS-LRMN, France and Dept. of Automatic Measurement and Control, Harbin Institute of Technology, China. Yuemin Zhu, Marc Robini and Isabelle Magnin are with CREATIS-LRMN; CNRS, UMR 5220; Inserm, U630; INSA-Lyon; Université de Lyon; Université Lyon 1, Villeurbanne, France. Wanyu Liu and Zhaobang Pu are with Automatic Measurement and Control, Harbin Institute of Technology, China. was developed from sparse representation [9]. In this paper, we propose a new method for filtering diffusion weighted (DW) images in cardiac DT-MRI. The method is based on sparse representation through using the BPDN algorithm allowing seeking overall sparest solution. It consists of sparsely representing useful structures in DW images with Heaviside dictionary, while yielding nonsparse representation on noise, which leads to the separation of the noise from the image’s useful structures. The proposed method is evaluated on both simulated and real images. The rest of the paper is organized into the following sections: In Section II, we briefly describe the sparse representation theory as well as the BPDN algorithm. In Section III, we present how the BPDN is applied to DW images in order to better compute diffusion tensors and eigenvectors. We discuss the obtained results and conclude in Section IV. II. SPARSE REPRENSENTATION Sparse representation is a theory for computing the representation coefficients, x, based on the given signal y and the dictionary T. Such approach, commonly referred to as “atom decomposition”, requires solving 0 min x subject to x, x y T = (1) and this is typically done by a “pursuit algorithm” that finds an approximate solution [10]. In the past decade, several efficient pursuit algorithms have been proposed, such as matching pursuit (MP), orthogonal matching pursuit (OMP), basis pursuit (BP), method of frames (MOF), and focal under- determined system solver (FOCUSS). Among them, the BP presents the particularity of adopting global optimization such that it allows obtaining the decomposition with high sparsity and super resolution. The BP algorithm finds the best representation of a signal by minimizing the 1-norm of the components of x, the coefficients in the representation. Assume that the input image to be decomposed is of size N×N. We represent this image as a one-dimensional (1D) vector of length N 2 by simple reordering as Y t . For such a vector Y t , we establish an over-complete representation matrix L N t M T × ∈ 2 , where L is the number of atoms in the dictionary (typically L  N 2 ), such that Analysis of Cardiac Diffusion Tensor Magnetic Resonance Images Using Sparse Representation Lijun Bao, Yuemin Zhu, Wanyu Liu, Marc Robini, Zhaobang Pu, Isabelle Magnin D Proceedings of the 29th Annual International Conference of the IEEE EMBS Cité Internationale, Lyon, France August 23-26, 2007. SaP1B4.12 1-4244-0788-5/07/$20.00 ©2007 IEEE 4516