Recent advances in the field of magnetic resonance (MR) based imaging of white matter (WM) have brought about the means to create extremely detailed 3D representations of WM architecture. These include advanced imaging techniques such as High Angular Resolution Imaging (HARDI) as well as sophisticated modeling and tractography algorithms. Tractography creates sets of “fibers” (3D streamlines), which represent the major pathways of neural connections. A full brain fiber set often contains half a million or more fibers and results in extremely large file (of the order of 1 GB). The storage problem is further exacerbated by the need to save fiber-sets for multiple brain scans, as is often the case in many studies and databases. There are several possible ways to approach this problem: smart coding of the original data to optimize bit allocations, omission of part of the fibers to minimize redundancies, which is a form of smart down-sampling of the dataset, or
© Springer International Publishing AG 2017
A. Fuster et al. (eds.), Computational Diffusion MRI, Mathematics
and Visualization, DOI 10.1007/978-3-319-54130-3_11
finding an alternative representation for the fibers themselves. Ultimately all three elements need to be combined to create a complete compression scheme for WM fiber sets. In recent years several works have addressed the issue of reducing the number of fibers [1, 2]. A complete compression pipeline with fiber representation and coding was presented in a work by Presseau et al. .
In this paper, we address the issue of compressing the fibers, or in other words we seek a fiber representation that requires less storage, while still providing a good approximation to the original fibers. This “compressed” representation is intended to serve as part of a lossy compression scheme. In addition, we strive to provide the means to evaluate similarities between fibers without explicitly returning to the original, uncompressed format. Calculation of inter-fiber distances or similarities is one of the frequently performed tasks in many algorithms for fiber clustering, classification, or registration. Allowing such calculations to be completed using the compressed representation will facilitate reduction in storage space and computational complexity. We propose to use sparse representations for fibers in a high dimensional space defined by overcomplete dictionary. This method of signal decomposition was shown to be beneficial to compression in various applications . Inter-fiber similarity can then be calculated directly in the compressed space, using sparse representations  and a specially tailored similarity measure— Cosine with Dictionary Similarity Weighting (CWDS), which we define below. The proposed method is shown in Sect. 2, followed by experimental validation in Sect. 3 and discussion and conclusions in Sect. 4.