Optimization of retinotopy constrained source estimation constrained by prior.
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ABSTRACT:
SUBMITTER: Hagler DJ
PROVIDER: S-EPMC4586264 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:Retinotopy constrained source estimation (RCSE) is a method for noninvasively measuring the time courses of activation in early visual areas using magnetoencephalography (MEG) or electroencephalography (EEG). Unlike conventional equivalent current dipole or distributed source models, the use of multiple, retinotopically mapped stimulus locations to simultaneously constrain the solutions allows for the estimation of independent waveforms for visual areas V1, V2, and V3, despite their close proximity to each other. We describe modifications that improve the reliability and efficiency of this method. First, we find that increasing the number and size of visual stimuli results in source estimates that are less susceptible to noise. Second, to create a more accurate forward solution, we have explicitly modeled the cortical point spread of individual visual stimuli. Dipoles are represented as extended patches on the cortical surface, which take into account the estimated receptive field size at each location in V1, V2, and V3 as well as the contributions from contralateral, ipsilateral, dorsal, and ventral portions of the visual areas. Third, we implemented a map fitting procedure to deform a template to match individual subject retinotopic maps derived from functional magnetic resonance imaging (fMRI). This improves the efficiency of the overall method by allowing automated dipole selection, and it makes the results less sensitive to physiological noise in fMRI retinotopy data. Finally, the iteratively reweighted least squares (IRLS) method was used to reduce the contribution from stimulus locations with high residual error for robust estimation of visual evoked responses.
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Project description:Despite evoked potentials' (EP) ubiquity in research and clinical medicine, insights are limited to gross brain dynamics as it remains challenging to map surface potentials to their sources in specific cortical regions. Multiple sources cancellation due to cortical folding and cross-talk obscures close sources, e.g. between visual areas V1 and V2. Recently retinotopic functional magnetic resonance imaging (fMRI) responses were used to constrain source locations to assist separating close sources and to determine cortical current generators. However, an fMRI is largely infeasible for routine EP investigation. We developed a novel method that replaces the fMRI derived retinotopic layout (RL) by an approach where the retinotopy and current estimates are generated from EEG or MEG signals and a standard clinical T1-weighted anatomical MRI. Using the EEG-RL, sources were localized to within 2 mm of the fMRI-RL constrained localized sources. The EEG-RL also produced V1 and V2 current waveforms that closely matched the fMRI-RL's (n = 2) r(1,198) = 0.99, P < 0.0001. Applying the method to subjects without fMRI (n = 4) demonstrates it generates waveforms that agree closely with the literature. Our advance allows investigators with their current EEG or MEG systems to create a library of brain models tuned to individual subjects' cortical folding in retinotopic maps, and should be applicable to auditory and somatosensory maps. The novel method developed expands EP's ability to study specific brain areas, revitalizing this well-worn technique. Hum Brain Mapp 37:1696-1709, 2016. © 2016 Wiley Periodicals, Inc.
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Project description:Many least-square problems involve affine equality and inequality constraints. Although there are a variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current article proposes a new path-following algorithm for quadratic programming that replaces hard constraints by what are called exact penalties. Similar penalties arise in l1 regularization in model selection. In the regularization setting, penalties encapsulate prior knowledge, and penalized parameter estimates represent a trade-off between the observed data and the prior knowledge. Classical penalty methods of optimization, such as the quadratic penalty method, solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ?, one recovers the constrained solution. In the exact penalty method, squared penalties!are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. The exact path-following method starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. Path following in Lasso penalized regression, in contrast, starts with a large value of the penalty constant and works its way downward. In both settings, inspection of the entire solution path is revealing. Just as with the Lasso and generalized Lasso, it is possible to plot the effective degrees of freedom along the solution path. For a strictly convex quadratic program, the exact penalty algorithm can be framed entirely in terms of the sweep operator of regression analysis. A few well-chosen examples illustrate the mechanics and potential of path following. This article has supplementary materials available online.
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Project description:Prior image constrained compressed sensing (PICCS) is an image reconstruction framework which incorporates an often available prior image into the compressed sensing objective function. The images are reconstructed using an optimization procedure. In this paper, several alternative unconstrained minimization methods are used to implement PICCS. The purpose is to study and compare the performance of each implementation, as well as to evaluate the performance of the PICCS objective function with respect to image quality.Six different minimization methods are investigated with respect to convergence speed and reconstruction accuracy. These minimization methods include the steepest descent (SD) method and the conjugate gradient (CG) method. These algorithms require a line search to be performed. Thus, for each minimization algorithm, two line searching algorithms are evaluated: a backtracking (BT) line search and a fast Newton-Raphson (NR) line search. The relative root mean square error is used to evaluate the reconstruction accuracy. The algorithm that offers the best convergence speed is used to study the performance of PICCS with respect to the prior image parameter α and the data consistency parameter λ. PICCS is studied in terms of reconstruction accuracy, low-contrast spatial resolution, and noise characteristics. A numerical phantom was simulated and an animal model was scanned using a multirow detector computed tomography (CT) scanner to yield the projection datasets used in this study.For λ within a broad range, the CG method with Fletcher-Reeves formula and NR line search offers the fastest convergence for an equal level of reconstruction accuracy. Using this minimization method, the reconstruction accuracy of PICCS was studied with respect to variations in α and λ. When the number of view angles is varied between 107, 80, 64, 40, 20, and 16, the relative root mean square error reaches a minimum value for α ≈ 0.5. For values of α near the optimal value, the spatial resolution of the reconstructed image remains relatively constant and the noise texture is very similar to that of the prior image, which was reconstructed using the filtered backprojection (FBP) algorithm.Regarding the performance of the minimization methods, the nonlinear CG method with NR line search yields the best convergence speed. Regarding the performance of the PICCS image reconstruction, three main conclusions can be reached. (1) The performance of PICCS is optimal when the weighting parameter of the prior image parameter is selected to be near α = 0.5. (2) The spatial resolution measured for static objects in images reconstructed using PICCS from undersampled datasets is not degraded with respect to the fully-sampled reconstruction for α near its optimal value. (3) The noise texture of PICCS reconstructions is similar to that of the prior image, which was reconstructed using the conventional FBP method.
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