| 1. |
- Karlsson, Johan, et al.
(författare)
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On Robustness of l(1)-Regularization Methods for Spectral Estimation
- 2014
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Ingår i: 2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781467360906 ; , s. 1767-1773, s. 1767-1773
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Konferensbidrag (refereegranskat)abstract
- The use of l(1)-regularization in sparse estimation methods has received huge attention during the last decade, and applications in virtually all fields of applied mathematics have benefited greatly. This interest was sparked by the recovery results of Cands, Donoho, Tao, Tropp, et al. and has resulted in a framework for solving a set of combinatorial problems in polynomial time by using convex relaxation techniques. In this work we study the use of l(1)-regularization methods for high-resolution spectral estimation. In this problem, the dictionary is typically coherent and existing theory for robust/exact recovery does not apply. In fact, the robustness cannot be guaranteed in the usual strong sense. Instead, we consider metrics inspired by the Monge-Kantorovich transportation problem and show that the magnitude can be robustly recovered if the original signal is sufficiently sparse and separated. We derive both worst case error bounds as well as error bounds based on assumptions on the noise distribution.
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| 2. |
- Ning, Lipeng, et al.
(författare)
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Cumulant expansions for measuring water exchange using diffusion MRI
- 2018
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 148:7
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Tidskriftsartikel (refereegranskat)abstract
- The rate of water exchange across cell membranes is a parameter of biological interest and can be measured by diffusion magnetic resonance imaging (dMRI). In this work, we investigate a stochastic model for the diffusion-and-exchange of water molecules. This model provides a general solution for the temporal evolution of dMRI signal using any type of gradient waveform, thereby generalizing the signal expressions for the Kärger model. Moreover, we also derive a general nth order cumulant expansion of the dMRI signal accounting for water exchange, which has not been explored in earlier studies. Based on this analytical expression, we compute the cumulant expansion for dMRI signals for the special case of single diffusion encoding (SDE) and double diffusion encoding (DDE) sequences. Our results provide a theoretical guideline on optimizing experimental parameters for SDE and DDE sequences, respectively. Moreover, we show that DDE signals are more sensitive to water exchange at short-time scale but provide less attenuation at long-time scale than SDE signals. Our theoretical analysis is also validated using Monte Carlo simulations on synthetic structures.
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| 3. |
- Ning, Lipeng, et al.
(författare)
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Precise Inference and Characterization of Structural Organization (PICASO) of tissue from molecular diffusion
- 2017
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Ingår i: NeuroImage. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 1053-8119 .- 1095-9572. ; 146, s. 452-473
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Tidskriftsartikel (refereegranskat)abstract
- Inferring the microstructure of complex media from the diffusive motion of molecules is a challenging problem in diffusion physics. In this paper, we introduce a novel representation of diffusion MRI (dMRI) signal from tissue with spatially-varying diffusivity using a diffusion disturbance function. This disturbance function contains information about the (intra-voxel) spatial fluctuations in diffusivity due to restrictions, hindrances and tissue heterogeneity of the underlying tissue substrate. We derive the short- and long-range disturbance coefficients from this disturbance function to characterize the tissue structure and organization. Moreover, we provide an exact relation between the disturbance coefficients and the time-varying moments of the diffusion propagator, as well as their relation to specific tissue microstructural information such as the intra-axonal volume fraction and the apparent axon radius. The proposed approach is quite general and can model dMRI signal for any type of gradient sequence (rectangular, oscillating, etc.) without using the Gaussian phase approximation. The relevance of the proposed PICASO model is explored using Monte-Carlo simulations and in-vivo dMRI data. The results show that the estimated disturbance coefficients can distinguish different types of microstructural organization of axons.
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| 4. |
- Ning, Lipeng, et al.
(författare)
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Probing tissue microstructure by diffusion skewness tensor imaging
- 2021
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Ingår i: Scientific Reports. - : Springer Science and Business Media LLC. - 2045-2322. ; 11:1
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Tidskriftsartikel (refereegranskat)abstract
- Probing the cellular structure of in vivo biological tissue is a fundamental problem in biomedical imaging and medical science. This work introduces an approach for analyzing diffusion magnetic resonance imaging data acquired by the novel tensor-valued encoding technique for characterizing tissue microstructure. Our approach first uses a signal model to estimate the variance and skewness of the distribution of apparent diffusion tensors modeling the underlying tissue. Then several novel imaging indices, such as weighted microscopic anisotropy and microscopic skewness, are derived to characterize different ensembles of diffusion processes that are indistinguishable by existing techniques. The contributions of this work also include a theoretical proof that shows that, to estimate the skewness of a diffusion tensor distribution, the encoding protocol needs to include full-rank tensor diffusion encoding. This proof provides a guideline for the application of this technique. The properties of the proposed indices are illustrated using both synthetic data and in vivo data acquired from a human brain.
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| 5. |
- Yamamoto, Kaoru, et al.
(författare)
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Regularization and Interpolation of Positive Matrices
- 2018
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286. ; 63:4, s. 1208-1212
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Tidskriftsartikel (refereegranskat)abstract
- We construct certain matricial analogues of mass transport for positive definite matrices of equal trace. The framework aims to devise ways of interpolating positive definite matrices that tradeoff between "aligning up their eigenstructure" and "scaling the corresponding eigenvalues". Motivation for the work is provided by power spectral analysis of multivariate time series where linear interpolation between matrix-valued power spectra generates push-pop unrealistic and undesirable artifacts.
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