Guangzhi Cao

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Covariance estimation for high dimensional vectors is a classically difficult problem in statistical analysis and machine learning. In this paper, we propose a maximum likelihood (ML) approach to covariance estimation, which employs a novel sparsity constraint. More specifically, the covariance is constrained to have an eigen decomposition which can be(More)
A variety of problems in remote sensing require that a covariance matrix be accurately estimated, often from a limited number of data samples. We investigate the utility of several variants of a recently introduced covariance estimator-the sparse matrix transform (SMT), a shrinkage-enhanced SMT, and a graph-constrained SMT-in the context of several of these(More)
Covariance estimation for high dimensional signals is a classically difficult problem in statistical signal analysis and machine learning. In this paper, we propose a maximum likelihood (ML) approach to covariance estimation, which employs a novel non-linear sparsity constraint. More specifically, the covariance is constrained to have an eigen decomposition(More)
Recently, the Sparse Matrix Transform (SMT) has been proposed as a tool for estimating the eigen-decomposition of high dimensional data vectors [1]. The SMT approach has two major advantages: First it can improve the accuracy of the eigendecomposition, particularlywhen the number of observations, n, is less the the vector dimension, p. Second, the resulting(More)
Many detection algorithms in hyperspectral image analysis, from well-characterized gaseous and solid targets to deliberately uncharacterized anomalies and anomalous changes, depend on accurately estimating the covariance matrix of the background. In practice, the background covariance is estimated from samples in the image, and imprecision in this estimate(More)
We present a method for noniterative maximum <i>a</i> <i>posteriori</i> (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large(More)
A barrier to the use of optical tomography in practical applications is the high computational cost of iterative image reconstruction. This paper introduces a novel method for direct reconstruction of the image from a pre-computed and stored inverse matrix. Since the inverse matrix for optical tomography is generally quite large and not sparse, it is(More)
Regression from high dimensional observation vectors is particularly difficult when training data is limited. More specifically, if the number of sample vectors n is less than dimension of the sample vectors p, then accurate regression is difficult to perform without prior knowledge of the data covariance. In this paper, we propose a novel approach to high(More)
Space-varying convolution often arises in the modeling or restoration of images captured by optical imaging systems. For example, in applications such as microscopy or photography the distortions introduced by lenses typically vary across the field of view, so accurate restoration also requires the use of space-varying convolution. While space-invariant(More)