Restoration of DWI Data Using a Rician LMMSE Estimator

This paper introduces and analyzes a linear minimum mean square error (LMMSE) estimator using a Rician noise model and its recursive version (RLMMSE) for the restoration of diffusion weighted images. A method to estimate the noise level based on local estimations of mean or variance is used to automatically parametrize the estimator. The restoration performance is evaluated using quality indexes and compared to alternative estimation schemes. The overall scheme is simple, robust, fast, and improves estimations. Filtering diffusion weighted magnetic resonance imaging (DW-MRI) with the proposed methodology leads to more accurate tensor estimations. Real and synthetic datasets are analyzed

The Convex Geometry of Linear Inverse Problems

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constrained structurally so that they only have a few degrees of freedom relative to their ambient dimension. This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems. The class of simple models considered are those formed as the sum of a few atoms from some (possibly infinite) elementary atomic set; examples include well-studied cases such as sparse vectors and low-rank matrices, as well as several others including sums of a few permutations matrices, low-rank tensors, orthogonal matrices, and atomic measures. The convex programming formulation is based on minimizing the norm induced by the convex hull of the atomic set; this norm is referred to as the atomic norm. The facial structure of the atomic norm ball carries a number of favorable properties that are useful for recovering simple models, and an analysis of the underlying convex geometry provides sharp estimates of the number of generic measurements required for exact and robust recovery of models from partial information. These estimates are based on computing the Gaussian widths of tangent cones to the atomic norm ball. When the atomic set has algebraic structure the resulting optimization problems can be solved or approximated via semidefinite programming. The quality of these approximations affects the number of measurements required for recovery. Thus this work extends the catalog of simple models that can be recovered from limited linear information via tractable convex programming

The QUIJOTE experiment: project status and first scientific results

We present the current status of the QUIJOTE (Q-U-I JOint TEnerife) experiment, a new polarimeter with the aim of characterizing the polarization of the Cosmic Microwave Background, and other galactic or extra-galactic physical processes that emit in microwaves in the frequency range 10–42 GHz, and at large angular scales (around 1 degree resolution). The experiment has been designed to reach the required sensitivity to detect a primordial gravitational wave component in the CMB, provided its tensor-to-scalar ratio is larger than r ∼ 0.05. The project consists of two telescopes and three instruments which will survey a large sky area from the Teide Observatory to provide I, Q and U maps of high sensitivity. The first QUIJOTE instrument, known as Multi-Frequency Instrument (MFI), has been surveying the northern sky in four individual frequencies between 10 and 20 GHz since November 2012, providing data with an average sensitivity of 80 µK beam−1 in Q and U in a region of 20, 000 square-degrees. The second instrument, or Thirty-GHz Instrument (TGI), is currently undergoing the commissioning phase, and the third instrument, or Forty-GHz Instrument (FGI), is in the final fabrication phase. Finally, we describe the first scientific results obtained with the MFI. Some specific regions, mainly along the Galactic plane, have been surveyed to a deeper depth, reaching sensitivities of around 40 µK beam−1. We present new upper limits on the polarization of the anomalous dust emission, resulting from these data, in the Perseus molecular complex and in the W43 molecular complex

The status of the Quijote multi-frequency instrument

The QUIJOTE-CMB project has been described in previous publications. Here we present the current status of the QUIJOTE multi-frequency instrument (MFI) with five separate polarimeters (providing 5 independent sky pixels): two which operate at 10-14 GHz, two which operate at 16-20 GHz, and a central polarimeter at 30 GHz. The optical arrangement includes 5 conical corrugated feedhorns staring into a dual reflector crossed-draconian system, which provides optimal cross-polarization properties (designed to be < -35 dB) and symmetric beams. Each horn feeds a novel cryogenic on-axis rotating polar modulator which can rotate at a speed of up to 1 Hz. The science driver for this first instrument is the characterization of the galactic emission. The polarimeters use the polar modulator to derive linear polar parameters Q, U and I and switch out various systematics. The detection system provides optimum sensitivity through 2 correlated and 2 total power channels. The system is calibrated using bright polarized celestial sources and through a secondary calibration source and antenna. The acquisition system, telescope control and housekeeping are all linked through a real-time gigabit Ethernet network. All communication, power and helium gas are passed through a central rotary joint. The time stamp is synchronized to a GPS time signal. The acquisition software is based on PLCs written in Beckhoffs TwinCat and ethercat. The user interface is written in LABVIEW. The status of the QUIJOTE MFI will be presented including pre-commissioning results and laboratory testing

Diffusion Weighted Image Denoising using overcomplete Local PCA

Diffusion Weighted Images (DWI) normally shows a low Signal to Noise Ratio (SNR) due to the presence of noise from the measurement process that complicates and biases the estimation of quantitative diffusion parameters. In this paper, a new denoising methodology is proposed that takes into consideration the multicomponent nature of multi-directional DWI datasets such as those employed in diffusion imaging. This new filter reduces random noise in multicomponent DWI by locally shrinking less significant Principal Components using an overcomplete approach. The proposed method is compared with state-of-the-art methods using synthetic and real clinical MR images, showing improved performance in terms of denoising quality and estimation of diffusion parameters.This work has been supported by the Spanish grant TIN2011-26727 from Ministerio de Ciencia e Innovacion. This work has been also partially supported by the French grant "HR-DTI" ANR-10-LABX-57 funded by the TRAIL from the French Agence Nationale de la Recherche within the context of the Investments for the Future program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Manjón Herrera, JV.; Coupé, P.; Concha, L.; Buades, A.; Collins, L.; Robles Viejo, M. (2013). Diffusion Weighted Image Denoising using overcomplete Local PCA. PLoS ONE. 8(9):1-12. https://doi.org/10.1371/journal.pone.0073021S11289Sundgren, P. C., Dong, Q., Gómez-Hassan, D., Mukherji, S. K., Maly, P., & Welsh, R. (2004). Diffusion tensor imaging of the brain: review of clinical applications. Neuroradiology, 46(5), 339-350. doi:10.1007/s00234-003-1114-xJohansen-Berg, H., & Behrens, T. E. (2006). Just pretty pictures? What diffusion tractography can add in clinical neuroscience. Current Opinion in Neurology, 19(4), 379-385. doi:10.1097/01.wco.0000236618.82086.01Jones DK, Basser PJ (2004) Squashing peanuts and smashing pumpkins: how noise distorts diffusion-weighted MR data. Magnetic Resonance in Medicine 52, 979–993.Chen, B., & Hsu, E. W. (2005). Noise removal in magnetic resonance diffusion tensor imaging. Magnetic Resonance in Medicine, 54(2), 393-401. doi:10.1002/mrm.20582Aja-Fernandez, S., Niethammer, M., Kubicki, M., Shenton, M. E., & Westin, C.-F. (2008). Restoration of DWI Data Using a Rician LMMSE Estimator. IEEE Transactions on Medical Imaging, 27(10), 1389-1403. doi:10.1109/tmi.2008.920609Basu S, Fletcher T, Whitaker R (2006) Rician noise removal in diffusion tensor MRI. MICCAI2006: 9,117–25.Hamarneh, G., & Hradsky, J. (2007). Bilateral Filtering of Diffusion Tensor Magnetic Resonance Images. IEEE Transactions on Image Processing, 16(10), 2463-2475. doi:10.1109/tip.2007.904964Xu, Q., Anderson, A. W., Gore, J. C., & Ding, Z. (2010). Efficient anisotropic filtering of diffusion tensor images. Magnetic Resonance Imaging, 28(2), 200-211. doi:10.1016/j.mri.2009.10.001Parker, G. J. M., Schnabel, J. A., Symms, M. R., Werring, D. J., & Barker, G. J. (2000). Nonlinear smoothing for reduction of systematic and random errors in diffusion tensor imaging. Journal of Magnetic Resonance Imaging, 11(6), 702-710. doi:10.1002/1522-2586(200006)11:63.0.co;2-aWeickert J, Brox T (2002) Diffusion and regularization of vector and matrix valued images. Saarland Department of Mathematics, Saarland University. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.195Wang, Z., Vemuri, B. C., Chen, Y., & Mareci, T. H. (2004). A Constrained Variational Principle for Direct Estimation and Smoothing of the Diffusion Tensor Field From Complex DWI. IEEE Transactions on Medical Imaging, 23(8), 930-939. doi:10.1109/tmi.2004.831218Reisert, M., & Kiselev, V. G. (2011). Fiber Continuity: An Anisotropic Prior for ODF Estimation. IEEE Transactions on Medical Imaging, 30(6), 1274-1283. doi:10.1109/tmi.2011.2112769Fillard, P., Pennec, X., Arsigny, V., & Ayache, N. (2007). Clinical DT-MRI Estimation, Smoothing, and Fiber Tracking With Log-Euclidean Metrics. IEEE Transactions on Medical Imaging, 26(11), 1472-1482. doi:10.1109/tmi.2007.899173Poon PK, Wei-Ren Ng, Sridharan V (2009) Image Denoising with Singular Value Decompositon and Principal Component Analysis. http://www.u.arizona.edu/~ppoon/ImageDenoisingWithSVD.pdfZhang, L., Dong, W., Zhang, D., & Shi, G. (2010). Two-stage image denoising by principal component analysis with local pixel grouping. Pattern Recognition, 43(4), 1531-1549. doi:10.1016/j.patcog.2009.09.023Deledalle C, Salmon J, Dalalyan A (2011) Image denoising with patch based PCA: local versus global. BMVC2011.Manjón JV, Thacker N, Lull JJ, Garcia-Martí G, Martí-Bonmatí L, et al.. (2009) Multicomponent MR Image Denoising. International Journal of Biomedical imaging, Article ID 756897.Bao, L., Robini, M., Liu, W., & Zhu, Y. (2013). Structure-adaptive sparse denoising for diffusion-tensor MRI. Medical Image Analysis, 17(4), 442-457. doi:10.1016/j.media.2013.01.006Strang G (1976) Linear Algebra and Its Applications Academic. New York,19802.Jolliffe IT (1986) Principal component analysis (Vol. 487). New York: Springer-Verlag.Manjón, J. V., Coupé, P., Buades, A., Louis Collins, D., & Robles, M. (2012). New methods for MRI denoising based on sparseness and self-similarity. Medical Image Analysis, 16(1), 18-27. doi:10.1016/j.media.2011.04.003Coifman R, Donoho DL (1995) Translation Invariant Denoising, Wavelets and Statistics. Anestis Antoniadis, ed. Springer Verlag Lecture Notes.Nowak, R. D. (1999). Wavelet-based Rician noise removal for magnetic resonance imaging. IEEE Transactions on Image Processing, 8(10), 1408-1419. doi:10.1109/83.791966Koay CG, Basser PJ (2006) Analytically exact correction scheme for signal extraction from noisy magnitude MR signals. J Magn Reson, 179,317–322.Coupé, P., Manjón, J. V., Gedamu, E., Arnold, D., Robles, M., & Collins, D. L. (2010). Robust Rician noise estimation for MR images. Medical Image Analysis, 14(4), 483-493. doi:10.1016/j.media.2010.03.001Close, T. G., Tournier, J.-D., Calamante, F., Johnston, L. A., Mareels, I., & Connelly, A. (2009). A software tool to generate simulated white matter structures for the assessment of fibre-tracking algorithms. NeuroImage, 47(4), 1288-1300. doi:10.1016/j.neuroimage.2009.03.077Coupe, P., Yger, P., Prima, S., Hellier, P., Kervrann, C., & Barillot, C. (2008). An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images. IEEE Transactions on Medical Imaging, 27(4), 425-441. doi:10.1109/tmi.2007.906087Manjón, J. V., Coupé, P., Martí-Bonmatí, L., Collins, D. L., & Robles, M. (2009). Adaptive non-local means denoising of MR images with spatially varying noise levels. Journal of Magnetic Resonance Imaging, 31(1), 192-203. doi:10.1002/jmri.22003Coupé P, Hellier P, Prima S, Kervrann C, Barillot C (2008) 3D Wavelet Subbands Mixing for Image Denoising. International Journal of Biomedical Imaging. Article ID 590183.Smith, S. M., Jenkinson, M., Woolrich, M. W., Beckmann, C. F., Behrens, T. E. J., Johansen-Berg, H., … Matthews, P. M. (2004). Advances in functional and structural MR image analysis and implementation as FSL. NeuroImage, 23, S208-S219. doi:10.1016/j.neuroimage.2004.07.051Basser, P. J., Mattiello, J., & Lebihan, D. (1994). Estimation of the Effective Self-Diffusion Tensor from the NMR Spin Echo. Journal of Magnetic Resonance, Series B, 103(3), 247-254. doi:10.1006/jmrb.1994.103

The QUIJOTE experiment: project status and first scientific results

We present the current status of the QUIJOTE (Q-U-I JOint TEnerife) experiment, a new polarimeter with the aim of characterizing the polarization of the Cosmic Microwave Background, and other galactic or extra-galactic physical processes that emit in microwaves in the frequency range 10–42 GHz, and at large angular scales (around 1 degree resolution). The experiment has been designed to reach the required sensitivity to detect a primordial gravitational wave component in the CMB, provided its tensor-to-scalar ratio is larger than r ∼ 0.05. The project consists of two telescopes and three instruments which will survey a large sky area from the Teide Observatory to provide I, Q and U maps of high sensitivity. The first QUIJOTE instrument, known as Multi-Frequency Instrument (MFI), has been surveying the northern sky in four individual frequencies between 10 and 20 GHz since November 2012, providing data with an average sensitivity of 80 µK beam−1 in Q and U in a region of 20, 000 square-degrees. The second instrument, or Thirty-GHz Instrument (TGI), is currently undergoing the commissioning phase, and the third instrument, or Forty-GHz Instrument (FGI), is in the final fabrication phase. Finally, we describe the first scientific results obtained with the MFI. Some specific regions, mainly along the Galactic plane, have been surveyed to a deeper depth, reaching sensitivities of around 40 µK beam−1. We present new upper limits on the polarization of the anomalous dust emission, resulting from these data, in the Perseus molecular complex and in the W43 molecular complex