Browsing by Author "Sing Long Collao, Carlos Alberto"

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    An analysis of reconstruction noise from undersampled 4D flow MRI
    (ELSEVIER SCI LTD, 2023) Partin, Lauren; Schiavazzi, Daniele E.; Sing Long Collao, Carlos Alberto
    Novel Magnetic Resonance (MR) imaging modalities can quantify hemodynamics but require long acquisition times, precluding its widespread use for early diagnosis of cardiovascular disease. To reduce acquisition times, flow reconstruction from undersampled data is routinely performed., Reconstructed anatomical and hemodynamic images may present visual artifacts. While some artifacts are reconstruction errors, and a consequence of undersampling, others are due to measurement noise or the random choice of samples. A reconstructed image becomes thus a random variable: its bias leads to systematic reconstruction errors, whereas its fluctuations may induce spatial correlations that may be misconstrued for visual information or that may carry to quantities of interest computed from the image. Although the former has been studied in the literature, the latter has not received as much attention., In this study, we investigate the theoretical properties of the random perturbations arising from the reconstruction process. To our knowledge, this is the first study on this topic. We perform numerical experiments on simulated flow, on aortic phantom flow, and on aortic flow. These show that the correlation length remains limited to two to three pixels when a Gaussian undersampling pattern is combined with l(1)-norm minimization methods. The correlation length may increase significantly for other undersampling patterns, higher undersampling factors (i.e., higher than 8x compression), and other reconstruction methods. Our findings suggest that the reconstruction method has a large impact on the correlation. As reconstruction methods are routinely used in practice, the impact of these random perturbations in practical applications merits further study.
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    Exact classification of nmr spectra from nmr signals
    (Institute of Electrical and Electronics Engineers Inc., 2024) Lehmann, Pedro Izquierdo; Xavier, Aline; Andia Kohnenkampf, Marcelo Edgardo; Sing Long Collao, Carlos Alberto
    Nuclear magnetic resonance (NMR) spectroscopy is routinely used to study the properties of matter. Therefore, different materials can be classified according to their NMR spectra. However, the NMR spectra cannot be observed directly, and only the NMR signal, which is a sum of complex exponentials, is directly observable in practice. A popular approach to recover the spectrum is to perform harmonic retrieval, i.e., to reconstruct exactly the spectrum from the NMR signal. However, even when this approach fails, the spectrum might still be classified accurately. In this work, we model the spectrum as an atomic measure to study the performance of classifying the spectrum from the NMR signal, and to determine how it degrades in the presence of additive noise and changes in field intensity. Although we focus on NMR signals, our results are broadly applicable to sum-of-exponential signals. We show numerical results illustrating our claims.
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    InVAErt networks: A data-driven framework for model synthesis and identifiability analysis
    (Elsevier B.V., 2024) Tong G.G.; Sing Long Collao, Carlos Alberto; Schiavazzi D.E.
    Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to other aspects of system analysis including model inversion and identifiability. We introduce InVAErt (pronounced invert) networks, a comprehensive framework for data-driven analysis and synthesis of parametric physical systems which uses a deterministic encoder and decoder to represent the forward and inverse solution maps, a normalizing flow to capture the probabilistic distribution of system outputs, and a variational encoder designed to learn a compact latent representation for the lack of bijectivity between inputs and outputs. We formally analyze how changes in the penalty coefficients affect the stationarity condition of the loss function, the phenomenon of posterior collapse, and propose strategies for latent space sampling, since we find that all these aspects significantly affect both training and testing performance. We verify our framework through extensive numerical examples, including simple linear, nonlinear, and periodic maps, dynamical systems, and spatio-temporal PDEs.