title: HARDI DATA DENOISING USING VECTORIAL TOTAL VARIATION AND LOGARITHMIC BARRIER.
abstract: In this work, we wish to denoise HARDI (High Angular Resolution Diffusion Imaging) data arising in medical brain imaging. Diffusion imaging is a relatively new and powerful method to measure the three-dimensional profile of water diffusion at each point in the brain. These images can be used to reconstruct fiber directions and pathways in the living brain, providing detailed maps of fiber integrity and connectivity. HARDI data is a powerful new extension of diffusion imaging, which goes beyond the diffusion tensor imaging (DTI) model: mathematically, intensity data is given at every voxel and at any direction on the sphere. Unfortunately, HARDI data is usually highly contaminated with noise, depending on the b-value which is a tuning parameter pre-selected to collect the data. Larger b-values help to collect more accurate information in terms of measuring diffusivity, but more noise is generated by many factors as well. So large b-values are preferred, if we can satisfactorily reduce the noise without losing the data structure. Here we propose two variational methods to denoise HARDI data. The first one directly denoises the collected data S, while the second one denoises the so-called sADC (spherical Apparent Diffusion Coefficient), a field of radial functions derived from the data. These two quantities are related by an equation of the form S = S(S)exp (-b · sADC) (in the noise-free case). By applying these two different models, we will be able to determine which quantity will most accurately preserve data structure after denoising. The theoretical analysis of the proposed models is presented, together with experimental results and comparisons for denoising synthetic and real HARDI data.
authors.affiliation: Department of Mathematics University of California, Irvine Irvine, CA 92697-3875, USA.
authors.forename: Yunho
authors.initials: Y
authors.lastname: Kim
authors.forename: Paul M
authors.initials: PM
authors.lastname: Thompson
authors.forename: Luminita A
authors.initials: LA
authors.lastname: Vese
references.citation: Magn Reson Med. 2005 Apr;53(4):866-76
references.pmid: 15799039
references.citation: J Magn Reson Imaging. 2006 Sep;24(3):478-88
references.pmid: 16897692
references.citation: Neuron. 2003 Dec 4;40(5):885-95
references.pmid: 14659088
references.citation: J Magn Reson B. 1996 Jun;111(3):209-19
references.pmid: 8661285
references.citation: Magn Reson Med. 2002 Oct;48(4):577-82
references.pmid: 12353272
references.citation: Magn Reson Med. 1994 Nov;32(5):579-83
references.pmid: 7808259
references.citation: Magn Reson Med. 2004 Dec;52(6):1358-72
references.pmid: 15562495
references.citation: Magn Reson Med. 2002 Jun;47(6):1083-99
references.pmid: 12111955
references.citation: Inf Process Med Imaging. 2009;21:515-27
references.pmid: 19694290
references.citation: Inverse Probl Imaging (Springfield). 2009 Nov;3(4):625-648
references.pmid: 36937497
references.citation: Neuroimage. 2007 Aug 1;37(1):164-76
references.pmid: 17570683
references.citation: IEEE Trans Pattern Anal Mach Intell. 2005 Apr;27(4):506-517
references.pmid: 15794157
references.citation: Radiology. 1986 Nov;161(2):401-7
references.pmid: 3763909
references.citation: Inf Process Med Imaging. 2007;20:308-19
references.pmid: 17633709
references.citation: IEEE Trans Med Imaging. 2008 Apr;27(4):442-56
references.pmid: 18390342
references.citation: Magn Reson Med. 1999 Sep;42(3):515-25
references.pmid: 10467296
references.citation: Eur J Radiol. 2009 Mar;69(3):454-8
references.pmid: 18162352
references.citation: IEEE Trans Image Process. 1998;7(3):304-9
references.pmid: 18276250
references.citation: Magn Reson Med. 2009 Jan;61(1):205-14
references.pmid: 19097208
references.citation: IEEE Trans Med Imaging. 2007 Nov;26(11):1464-71
references.pmid: 18041262
references.citation: Inf Process Med Imaging. 2007;20:172-82
references.pmid: 17633698
references.citation: Proc IEEE Int Symp Biomed Imaging. 2006;2006:65-68
references.pmid: 19759891
references.citation: Neuroimage. 2009 Mar;45(1 Suppl):S111-22
references.pmid: 19063977
references.citation: Magn Reson Med. 2007 Sep;58(3):497-510
references.pmid: 17763358
references.citation: Proc IEEE Comput Soc Conf Comput Vis Pattern Recognit. 2007 Jul 16;2007(17-22 June 2007):1-7
references.pmid: 21311729
references.citation: Inf Process Med Imaging. 2005;19:311-20
references.pmid: 17354705