Penalized partially linear models using sparse representations with an application to fMRI time series

Fadili, Jalal M.; Bullmore, Edward T.

doi:10.1109/tsp.2005.853207

Cited by 28 publications

(44 citation statements)

References 36 publications

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“…The penalty term in (21) penalizes only the wavelet coefficients of the nonparametric part of the model and not the scaling coefficients. The penalized wavelet estimator (20) can be regarded as an extension of the wavelet shrinkage estimators, which are typically processed in batch form by iterative soft-thresholding algorithms [14,22,23]. However, the batch estimators suffer from high computational complexity and increased memory requirements as time progresses and are thus not appropriate for online implementation.…”

Section: Recursive Penalized Wavelet Estimator For Online Plbm Identimentioning

confidence: 99%

“…One attractive approach to solve such an optimization problem is to run an online CCD algorithm due to its speed and numerical stability [30,31]. The CCD algorithm separately minimizes the cost function (22) for each entry of β and can admit a closed-form solution.…”

Section: Recursive Penalized Wavelet Estimator For Online Plbm Identimentioning

confidence: 99%

“…Since the introductory work of Engle in 1986 [12], the semiparametric model has been widely studied and applied in many fields, such as applied statistics [13], signal processing [14,22], and dynamic system modeling [23][24][25]. However, to our knowledge, this model has not yet been investigated for use in battery modeling.…”

Section: Introductionmentioning

confidence: 99%

“…For the PLBM, an efficient estimation procedure must be developed for both the linear parameters and nonparametric component. Several semiparametric estimators [14,[22][23][24][25] based on basis function expansion methods have been proposed to identify the partially linear model. The current study is concerned with modeling the nonparametric component in the PLBM using the wavelet multiresolution analysis (MRA) expansion due to the wavelet's good time-frequency localization property.…”

Section: Introductionmentioning

confidence: 99%

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Online Semiparametric Identification of Lithium-Ion Batteries Using the Wavelet-Based Partially Linear Battery Model

Jiang

Zhang

2013

Energies

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Abstract:Battery model identification is very important for reliable battery management as well as for battery system design process. The common problem in identifying battery models is how to determine the most appropriate mathematical model structure and parameterized coefficients based on the measured terminal voltage and current. This paper proposes a novel semiparametric approach using the wavelet-based partially linear battery model (PLBM) and a recursive penalized wavelet estimator for online battery model identification. Three main contributions are presented. First, the semiparametric PLBM is proposed to simulate the battery dynamics. Compared with conventional electrical models of a battery, the proposed PLBM is equipped with a semiparametric partially linear structure, which includes a parametric part (involving the linear equivalent circuit parameters) and a nonparametric part [involving the open-circuit voltage (OCV)]. Thus, even with little prior knowledge about the OCV, the PLBM can be identified using a semiparametric identification framework. Second, we model the nonparametric part of the PLBM using the truncated wavelet multiresolution analysis (MRA) expansion, which leads to a parsimonious model structure that is highly desirable for model identification; using this model, the PLBM could be represented in a linear-in-parameter manner. Finally, to exploit the sparsity of the wavelet MRA representation and allow for online implementation, a penalized wavelet estimator that uses a modified online cyclic coordinate descent algorithm is proposed to identify the PLBM in a recursive fashion. The simulation and experimental results demonstrate that the proposed PLBM with the corresponding identification algorithm can accurately simulate the dynamic behavior of a lithium-ion battery in the Federal Urban Driving Schedule tests.

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Section: Recursive Penalized Wavelet Estimator For Online Plbm Identimentioning

confidence: 99%

Section: Recursive Penalized Wavelet Estimator For Online Plbm Identimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Online Semiparametric Identification of Lithium-Ion Batteries Using the Wavelet-Based Partially Linear Battery Model

Jiang

Zhang

2013

Energies

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“…Wavelet-based characterization of multi-fractal behavior for fMRI has been proposed [27]. Finally, estimation with the use of penalized partial linear models and classical wavelets has been investigated in [28].…”

Section: Wavelets and Fmrimentioning

confidence: 99%

Activelets: Wavelets for sparse representation of hemodynamic responses

et al. 2011

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a b s t r a c tWe propose a new framework to extract the activity-related component in the BOLD functional magnetic resonance imaging (fMRI) signal. As opposed to traditional fMRI signal analysis techniques, we do not impose any prior knowledge of the event timing. Instead, our basic assumption is that the activation pattern is a sequence of short and sparsely distributed stimuli, as is the case in slow event-related fMRI.We introduce new wavelet bases, termed ''activelets'', which sparsify the activityrelated BOLD signal. These wavelets mimic the behavior of the differential operator underlying the hemodynamic system. To recover the sparse representation, we deploy a sparse-solution search algorithm.The feasibility of the method is evaluated using both synthetic and experimental fMRI data. The importance of the activelet basis and the non-linear sparse recovery algorithm is demonstrated by comparison against classical B-spline wavelets and linear regularization, respectively.

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Detection and characterization of single‐trial fMRI bold responses: Paradigm free mapping

Caballero-Gaudes¹,

Petridou²,

Dryden³

et al. 2010

Human Brain Mapping

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This work presents a novel method of mapping the brain's response to single stimuli in space and time without prior knowledge of the paradigm timing: paradigm free mapping (PFM). This method is based on deconvolution of the hemodynamic response from the voxel time series assuming a linear response and using a ridge-regression algorithm. Statistical inference is performed by defining a spatio-temporal t-statistic and by controlling for multiple comparisons using the false discovery rate procedure. The methodology was validated on five subjects who performed self-paced and visually cued finger tapping at 7 Tesla, with moderate (TR = 2 s) and high (TR = 0.4 s) temporal resolution. The results demonstrate that detection of single-trial BOLD events is feasible without a priori information on the stimulus paradigm. The proposed method opens up the possibility of designing temporally unconstrained paradigms to study the cortical response to unpredictable mental events.

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Penalized partially linear models using sparse representations with an application to fMRI time series

Cited by 28 publications

References 36 publications

Online Semiparametric Identification of Lithium-Ion Batteries Using the Wavelet-Based Partially Linear Battery Model

Online Semiparametric Identification of Lithium-Ion Batteries Using the Wavelet-Based Partially Linear Battery Model

Activelets: Wavelets for sparse representation of hemodynamic responses

Detection and characterization of single‐trial fMRI bold responses: Paradigm free mapping

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