Revisiting the T2 spectrum imaging inverse problem: Bayesian regularized non-negative least squares
Erick Jorge Canales-Rodríguez,
Marco Pizzolato,
Thomas Yu,
Gian Franco Piredda,
Tom Hilbert,
Joaquim Radua,
Tobias Kober,
Jean-Philippe Thiran
Affiliations
Erick Jorge Canales-Rodríguez
Signal Processing Laboratory (LTS5), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-STI-IEL-LTS5, Station 11, CH-1015, Lausanne, Switzerland; Corresponding author.
Marco Pizzolato
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark; Signal Processing Laboratory (LTS5), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-STI-IEL-LTS5, Station 11, CH-1015, Lausanne, Switzerland
Thomas Yu
Signal Processing Laboratory (LTS5), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-STI-IEL-LTS5, Station 11, CH-1015, Lausanne, Switzerland; Medical Image Analysis Laboratory, Center for Biomedical Imaging (CIBM), University of Lausanne, Switzerland
Gian Franco Piredda
Signal Processing Laboratory (LTS5), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-STI-IEL-LTS5, Station 11, CH-1015, Lausanne, Switzerland; Advanced Clinical Imaging Technology, Siemens Healthcare AG, Lausanne, Switzerland; Department of Radiology, Lausanne University Hospital and University of Lausanne, Lausanne, Switzerland
Tom Hilbert
Signal Processing Laboratory (LTS5), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-STI-IEL-LTS5, Station 11, CH-1015, Lausanne, Switzerland; Advanced Clinical Imaging Technology, Siemens Healthcare AG, Lausanne, Switzerland; Department of Radiology, Lausanne University Hospital and University of Lausanne, Lausanne, Switzerland
Joaquim Radua
Imaging of Mood- and Anxiety-Related Disorders (IMARD) group, Institut d'Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), CIBERSAM, Barcelona, Spain; Department of Psychosis Studies, Institute of Psychiatry, Psychology, and Neuroscience, King's College London, London, United Kingdom; Department of Clinical Neuroscience, Centre for Psychiatric Research and Education, Karolinska Institutet, Stockholm, Sweden
Tobias Kober
Signal Processing Laboratory (LTS5), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-STI-IEL-LTS5, Station 11, CH-1015, Lausanne, Switzerland; Advanced Clinical Imaging Technology, Siemens Healthcare AG, Lausanne, Switzerland; Department of Radiology, Lausanne University Hospital and University of Lausanne, Lausanne, Switzerland
Jean-Philippe Thiran
Signal Processing Laboratory (LTS5), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-STI-IEL-LTS5, Station 11, CH-1015, Lausanne, Switzerland; Department of Radiology, Lausanne University Hospital and University of Lausanne, Lausanne, Switzerland
Multi-echo T2 magnetic resonance images contain information about the distribution of T2 relaxation times of compartmentalized water, from which we can estimate relevant brain tissue properties such as the myelin water fraction (MWF). Regularized non-negative least squares (NNLS) is the tool of choice for estimating non-parametric T2 spectra. However, the estimation is ill-conditioned, sensitive to noise, and highly affected by the employed regularization weight. The purpose of this study is threefold: first, we want to underline that the apparently innocuous use of two alternative parameterizations for solving the inverse problem, which we called the standard and alternative regularization forms, leads to different solutions; second, to assess the performance of both parameterizations; and third, to propose a new Bayesian regularized NNLS method (BayesReg). The performance of BayesReg was compared with that of two conventional approaches (L-curve and Chi-square (X2) fitting) using both regularization forms. We generated a large dataset of synthetic data, acquired in vivo human brain data in healthy participants for conducting a scan-rescan analysis, and correlated the myelin content derived from histology with the MWF estimated from ex vivo data. Results from synthetic data indicate that BayesReg provides accurate MWF estimates, comparable to those from L-curve and X2, and with better overall stability across a wider signal-to-noise range. Notably, we obtained superior results by using the alternative regularization form. The correlations reported in this study are higher than those reported in previous studies employing the same ex vivo and histological data. In human brain data, the estimated maps from L-curve and BayesReg were more reproducible. However, the T2 spectra produced by BayesReg were less affected by over-smoothing than those from L-curve. These findings suggest that BayesReg is a good alternative for estimating T2 distributions and MWF maps.
