Spatial variation decomposition via sparse regression

In this paper, we briefly discuss the recent development of a novel sparse regression technique that aims to accurately decompose process variation into two different components: (1) spatially correlated variation, and (2) uncorrelated random variation. Such variation decomposition is important to identify systematic variation patterns at wafer and/or chip level for process modeling, control and diagnosis. We demonstrate that the spatially correlated variation can be accurately represented by the linear combination of a small number of “templates”. Based upon this observation, an efficient algorithm is developed to accurately separate spatially correlated variation from uncorrelated random variation. Several examples based on silicon measurement data demonstrate that the aforementioned sparse regression technique can capture systematic variation patterns with high accuracy.Interconnect Focus Center (United States. Defense Advanced Research Projects Agency and Semiconductor Research Corporation)Focus Center Research Program. Focus Center for Circuit & System SolutionsNational Science Foundation (U.S.) (Contract CCF-0915912

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Dynamics and sparsity in latent threshold factor models: A study in multivariate EEG signal processing

We discuss Bayesian analysis of multivariate time series with dynamic factor models that exploit time-adaptive sparsity in model parametrizations via the latent threshold approach. One central focus is on the transfer responses of multiple interrelated series to underlying, dynamic latent factor processes. Structured priors on model hyper-parameters are key to the efficacy of dynamic latent thresholding, and MCMC-based computation enables model fitting and analysis. A detailed case study of electroencephalographic (EEG) data from experimental psychiatry highlights the use of latent threshold extensions of time-varying vector autoregressive and factor models. This study explores a class of dynamic transfer response factor models, extending prior Bayesian modeling of multiple EEG series and highlighting the practical utility of the latent thresholding concept in multivariate, non-stationary time series analysis.Comment: 27 pages, 13 figures, link to external web site for supplementary animated figure