title: Blind compressive sensing dynamic MRI.
abstract: We propose a novel blind compressive sensing (BCS) frame work to recover dynamic magnetic resonance images from undersampled measurements. This scheme models the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. In contrast to classical compressed sensing, the BCS scheme simultaneously estimates the dictionary and the sparse coefficients from the undersampled measurements. Apart from the sparsity of the coefficients, the key difference of the BCS scheme with current low rank methods is the nonorthogonal nature of the dictionary basis functions. Since the number of degrees-of-freedom of the BCS model is smaller than that of the low-rank methods, it provides improved reconstructions at high acceleration rates. We formulate the reconstruction as a constrained optimization problem; the objective function is the linear combination of a data consistency term and sparsity promoting l1 prior of the coefficients. The Frobenius norm dictionary constraint is used to avoid scale ambiguity. We introduce a simple and efficient majorize-minimize algorithm, which decouples the original criterion into three simpler subproblems. An alternating minimization strategy is used, where we cycle through the minimization of three simpler problems. This algorithm is seen to be considerably faster than approaches that alternates between sparse coding and dictionary estimation, as well as the extension of K-SVD dictionary learning scheme. The use of the l1 penalty and Frobenius norm dictionary constraint enables the attenuation of insignificant basis functions compared to the l0 norm and column norm constraint assumed in most dictionary learning algorithms; this is especially important since the number of basis functions that can be reliably estimated is restricted by the available measurements. We also observe that the proposed scheme is more robust to local minima compared to K-SVD method, which relies on greedy sparse coding. Our phase transition experiments demonstrate that the BCS scheme provides much better recovery rates than classical Fourier-based CS schemes, while being only marginally worse than the dictionary aware setting. Since the overhead in additionally estimating the dictionary is low, this method can be very useful in dynamic magnetic resonance imaging applications, where the signal is not sparse in known dictionaries. We demonstrate the utility of the BCS scheme in accelerating contrast enhanced dynamic data. We observe superior reconstruction performance with the BCS scheme in comparison to existing low rank and compressed sensing schemes.
authors.affiliation: Department of Biomedical Engineering, The University of Iowa, IA 52242 USA. sajangoud-lingala@uiowa.edu
authors.forename: Sajan Goud
authors.initials: SG
authors.lastname: Lingala
authors.forename: Mathews
authors.initials: M
authors.lastname: Jacob
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology / Q000502:physiology; D003198:Computer Simulation; D006321:Heart / Q000033:anatomy & histology / Q000502:physiology; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D019047:Phantoms, Imaging; D012815:Signal Processing, Computer-Assisted
references.citation: Magn Reson Med. 2007 Dec;58(6):1182-95
references.pmid: 17969013
references.citation: Magn Reson Med. 2009 Sep;62(3):706-16
references.pmid: 19585603
references.citation: Magn Reson Med. 2010 Jan;63(1):68-78
references.pmid: 19859952
references.citation: IEEE Trans Med Imaging. 2011 May;30(5):1042-54
references.pmid: 21292593
references.citation: IEEE Trans Med Imaging. 2011 May;30(5):1028-41
references.pmid: 21047708
references.citation: IEEE Trans Image Process. 2011 Mar;20(3):681-95
references.pmid: 20840899
references.citation: IEEE Trans Image Process. 2009 Jan;18(1):27-35
references.pmid: 19095516
references.citation: IEEE Trans Image Process. 2012 Feb;21(2):742-53
references.pmid: 21859601
references.citation: Magn Reson Med. 2003 Nov;50(5):1031-42
references.pmid: 14587014
references.citation: IEEE Trans Med Imaging. 2012 Sep;31(9):1809-20
references.pmid: 22695345
references.citation: Magn Reson Med. 2010 Sep;64(3):767-76
references.pmid: 20535813
references.citation: Magn Reson Med. 2008 Feb;59(2):365-73
references.pmid: 18228595
references.citation: IEEE Trans Med Imaging. 2011 Mar;30(3):694-706
references.pmid: 21095861
references.citation: IEEE Trans Image Process. 2008 Sep;17(9):1540-54
references.pmid: 18701393
references.citation: Proc IEEE Int Symp Biomed Imaging. 2012;:1060-1063
references.pmid: 24663291
references.citation: Magn Reson Med. 2010 Oct;64(4):1162-70
references.pmid: 20564601
references.citation: Magn Reson Med. 2010 Dec;64(6):1592-8
references.pmid: 20928891
references.citation: IEEE Trans Image Process. 2012 Aug;21(8):3659-72
references.pmid: 22531764
references.citation: IEEE Trans Image Process. 2006 Dec;15(12):3736-45
references.pmid: 17153947