On the optimal reconstruction of dMRI images with multi-coil acquisition system Farid AHMED SID and Fatima OULEBSIR-BOUMGHAR ParIM´ ed/LRPE, FEI, USTHB BP 32 El Alia, Bab Ezzouar, 16111 Algiers, Algeria Email: ahmedsid.f@gmail.com fboumghar@usthb.dz Karim ABED-MERAIM and Rachid HARBA PRISME Laboratory, University of Orl´ eans 12 Rue de Blois, 45067 Orl´ eans, France Email: karim.abed-meraim@univ-orleans.fr rachid.harba@univ-orleans.fr Abstract—In this paper, we consider a multi-coil diffusion MRI system and compare the achievable performance bounds for two image reconstruction methods using, respectively, the Matched Filtering (MF) and the Sum-of-Squares (SoS) techniques. This performance comparison is related to the parameter estimation accuracy of the multi-tensor diffusion model expressed in terms of Cram´ er-Rao Bounds (CRB). In particular, this analysis allows us to thoroughly quantify the large gain in favor of the MF approach and to illustrate the significant acquisition time reduction we can obtain if we replace the standard SoS technique by the MF-based one. Index Terms—Cram´ er-Rao Bound, matched filter, sum-of- squares, Nc-Chi distribution, DT model. I. I NTRODUCTION Diffusion Magnetic Resonance Imaging (dMRI) is an MRI modality, able to estimate, in-vivo and non invasive manner, the white matter local direction, by the observation of the mean displacement of water molecules at each voxel. dMRI has been used to study brain connectivity by using tractography algo- rithms (for a review, see [1]), or to diagnose neurodegenerative diseases like multiple scleroses, Alzheimer, or tumors (for a review, see [2], [3]). The majority of currently operated clinical MRI scanners, are equipped with multiple receiver coils, for the acquisition/transmission of the signal from/to the patient. Depending on the technique used to combine information from these coils, the noise properties change in the reconstructed image. For the standard image reconstruction technique used in the majority of MRI scanners, namely the sum-of-squares (SoS), the noise follows a non-central chi distribution [4], [5]. It is well established that this reconstruction method is not the SNR-optimal method. The optimal SNR (Signal- to-Noise Ratio) reconstruction technique is the one based Matched Filter (MF) [6], [7]. It has been shown in [8] that it is important to make the appropriate image reconstruction method from dMRI raw data in order to correctly estimate the fiber orientations and therefore the correct tractography. This is due to the fact that the SNR in dMRI is intrinsically low and the signal attenuation can be close to the noise floor [9]. In this study, using the Cram´ er-Rao Bound (CRB) tool, we provide a thorough comparison between the MF-based and SoS-based reconstruction techniques and highlight the significant gain we can obtain in dMRI model parameter estimation when using the MF approach. II. DATA MODEL A. The MR signal model Currently operated clinical MRI scanners are equipped with multichannel receiver coils, where each coil, after demodula- tion and filtering gives two signals treated as the real and imaginary parts of a complex raw data. Afterwards, the two- dimensional inverse discrete Fourier transform, of the raw data, results in L> 1 complex images in the image space, L being the number of coils. We denote by μ the complex image voxel intensity in the absence of noise, and by s the measured voxel intensity. If we assume that no magnetic coupling between the acquisition coils then, the complex signal intensity measured in one voxel of the l th coil can be expressed as s l = μ l + n l , (1) where n l is an additive complex white Gaussian noise process with zero-mean and variance σ 2 . Noise terms at different channels are uncorrelated, i.e. E(n l (t)n ∗ l ′ (t)) = 0 for l = l ′ . In arrays of receiver coils, a strong signal intensity is measured for voxels located close to the coil, and diminishes with distance, this property is designated by coil sensitivity, which mean that, the signal given by each coil is weighted by the coil sensitivity. So, the noise-free signal μ l can be seen as an original image A, a real value representing the desired MR contrast, weighted by the coil’s sensitivity c l (complex value) so that (1) becomes: s l = c l A + n l . (2) Note that if the main field is not homogeneous and/or the sample is a moving tissue, the realness assumption of the original image A will not held. Instead, a complex image A must be considered. In our work we have assumed that the image phase is taken into account in the coil sensitivities, this allows as to take A as a real quantity. In compact form, the set of measures can be denoted by s = cA + n, (3) 2016 24th European Signal Processing Conference (EUSIPCO) 978-0-9928-6265-7/16/$31.00 ©2016 IEEE 1318