12,680 research outputs found
Fast reconstruction of 3D blood flows from Doppler ultrasound images and reduced models
This paper deals with the problem of building fast and reliable 3D
reconstruction methods for blood flows for which partial information is given
by Doppler ultrasound measurements. This task is of interest in medicine since
it could enrich the available information used in the diagnosis of certain
diseases which is currently based essentially on the measurements coming from
ultrasound devices. The fast reconstruction of the full flow can be performed
with state estimation methods that have been introduced in recent years and
that involve reduced order models. One simple and efficient strategy is the
so-called Parametrized Background Data-Weak approach (PBDW). It is a linear
mapping that consists in a least squares fit between the measurement data and a
linear reduced model to which a certain correction term is added. However, in
the original approach, the reduced model is built a priori and independently of
the reconstruction task (typically with a proper orthogonal decomposition or a
greedy algorithm). In this paper, we investigate the construction of other
reduced spaces which are built to be better adapted to the reconstruction task
and which result in mappings that are sometimes nonlinear. We compare the
performance of the different algorithms on numerical experiments involving
synthetic Doppler measurements. The results illustrate the superiority of the
proposed alternatives to the classical linear PBDW approach
Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series
The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.National Science Foundation (IIS 0308213, IIS 0329009, CNS 0202067
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