Are Charles Jensen

Fast Hyperspectral Feature Reduction Using Piecewise Constant Function Approximations

The high number of spectral bands that are obtained from hyperspectral sensors, combined with the often limited ground truth, solicits some kind of feature reduction when attempting supervised classification. This letter demonstrates that an optimal constant function representation of hyperspectral signature curves in the mean square sense is capable of representing the data sufficiently to outperform, or match, other feature reduction methods such as principal components transform, sequential forward selection, and decision boundary feature extraction for classification purposes on all of the four hyperspectral data sets that we have tested. The simple averaging of spectral bands makes the resulting features directly interpretable in a physical sense. Using an efficient dynamic programming algorithm, the proposed method can be considered fast.

Sparse Inverse Covariance Estimates for Hyperspectral Image Classification

Classification of remotely sensed hyperspectral images calls for a classifier that gracefully handles high-dimensional data, where the amount of samples available for training might be very low relative to the dimension. Even when using simple parametric classifiers such as the Gaussian maximum-likelihood rule, the large number of bands leads to copious amounts of parameters to estimate. Most of these parameters are measures of correlations between features. The covariance structure of a multivariate normal population can be simplified by setting elements of the inverse covariance matrix to zero. Well-known results from time series analysis relates the estimation of the inverse covariance matrix to a sequence of regressions by using the Cholesky decomposition. We observe that discriminant analysis can be performed without inverting the covariance matrix. We propose defining a sparsity pattern on the lower triangular matrix resulting from the Cholesky decomposition, and develop a simple search algorithm for choosing this sparsity. The resulting classifier is used on four different hyperspectral images, and compared with conventional approaches such as support vector machines, with encouraging results

An approach to multibeam covariance matrices for adaptive beamforming in ultrasonography

Medical ultrasound imaging systems are often based on transmitting, and recording the backscatter from, a series of focused broadband beams with overlapping coverage areas. When applying adaptive beamforming, a separate array covariance matrix for each image sample is usually formed. The data used to estimate any one of these covariance matrices is often limited to the recorded backscatter from a single transmitted beam, or that of some adjacent beams through additional focusing at reception. We propose to form, for each radial distance, a single covariance matrix covering all of the beams. The covariance matrix is estimated by combining the array samples after a sequenced time delay and phase shift. The time delay is identical to that performed in conventional delay-and-sum beamforming. The performance of the proposed approach in conjunction with the Capon beamformer is studied on both simulated data of scenes consisting of point targets and recorded ultrasound phantom data from a specially adapted commercial scanner. The results show that the proposed approach is more capable of resolving point targets and gives better defined cyst-like structures in speckle images compared with the conventional delay-and-sum approach. Furthermore, it shows both an increased robustness to noise and an increased ability to resolve point-like targets compared with the more traditional per-beam Capon beamformer.

Semi-Supervised Nearest Mean Classification Through a Constrained Log-Likelihood

We cast a semi-supervised nearest mean classifier, previously introduced by the first author, in a more principled log-likelihood formulation that is subject to constraints. This, in turn, leads us to make the important suggestion to not only investigate error rates of semi-supervised learners but also consider the risk they originally aim to optimize. We demonstrate empirically that in terms of classification error, mixed results are obtained when comparing supervised to semi-supervised nearest mean classification, while in terms of log-likelihood on the test set, the semi-supervised method consistently outperforms its supervised counterpart. Comparisons to self-learning, a standard approach in semi-supervised learning, are included to further clarify the way, in which our constrained nearest mean classifier improves over regular, supervised nearest mean classification.

Applying Thomson's multitaper approach to reduce speckle in medical ultrasound imaging

To reduce the variance of speckle in coherent imaging systems, one must average images with different speckle realizations. Traditionally, these images have been formed by observing the target region from slightly different angles (spatial compounding) or by varying the involved temporal frequencies (frequency compounding). In this paper, we investigate a third option based on Thomsons multitaper approach to power spectrum estimation. The tapers are applied spatially, as array weights. Our investigations, based on both recorded ultrasound data and simulations, verify that the multitaper approach can be used for speckle reduction at a rate comparable to that of the more traditional method of spatial compounding. Because of the spectral concentration of the tapers, an added benefit is reduced side lobe levels, which can result in steeper edges and better definition of cyst-like structures.

Coherent plane-wave compounding and minimum variance beamforming

Achieving increased frame rate without compromising the image quality is desirable in medical ultrasound imaging. Coherent plane-wave compounding has recently been suggested as an approach to achieve this. This work proposes to generate coherent compound plane-wave images using a minimum variance adaptive beamformer. Through simulations of point scatterers and cyst phantoms, a threefold increase in frame rate is shown.

Regression approaches to small sample inverse covariance matrix estimation for hyperspectral image classification

A key component in most parametric classifiers is the estimation of an inverse covariance matrix. In hyperspectral images, the number of bands can be in the hundreds, leading to covariance matrices having tens of thousands of elements. Lately, the use of linear regression in estimating the inverse covariance matrix has been introduced in the time-series literature. This paper adopts and expands these ideas to ill-posed hyperspectral image classification problems. The results indicate that at least some of the approaches can give a lower classification error than traditional methods such as the linear discriminant analysis and the regularized discriminant analysis. Furthermore, the results show that, contrary to earlier beliefs, estimating long-range dependencies between bands appears necessary to build an effective hyperspectral classifier and that the high correlations between neighboring bands seem to allow differing sparsity configurations of the inverse covariance matrix to obtain similar classification results.

The iterative adaptive approach in medical ultrasound imaging

Many medical ultrasound imaging systems are based on sweeping the image plane with a set of narrow beams. Usually, the returning echo from each of these beams is used to form one or a few azimuthal image samples. We model, for each radial distance, jointly the full azimuthal scanline. The model consists of the amplitudes of a set of densely placed potential reflectors (or scatterers), cf. sparse signal representation. To fit the model, we apply the iterative adaptive approach (IAA) on data formed by a sequenced time delay and phase shift. The performance of the IAA in combination with our time-delayed and phase-shifted data are studied on both simulated data of scenes consisting of point targets and hollow cyst-like structures, and recorded ultrasound phantom data from a specially adapted commercially available scanner. The results show that the proposed IAA is more capable of resolving point targets and gives better defined and more geometrically correct cyst-like structures in speckle images compared with the conventional delay-and-sum (DAS) approach. Compared with a Capon beamformer, the IAA showed an improved rendering of cyst-like structures and a similar point-target resolvability. Unlike the Capon beamformer, the IAA has no user parameters and seems unaffected by signal cancellation. The disadvantage of the IAA is a high computational load.

Using Multiscale Spectra in Regularizing Covariance Matrices for Hyperspectral Image Classification

An important component in many supervised classifiers is the estimation of one or more covariance matrices, and the often low training-sample count in supervised hyperspectral image classification yields the need for strong regularization when estimating such matrices. Often, this regularization is accomplished through adding some kind of scaled regularization matrix, e.g., the identity matrix, to the sample covariance matrix. We introduce a framework for specifying and interpreting a broad range of such regularization matrices in the linear and quadratic discriminant analysis (LDA and QDA, respectively) classifier settings. A key component in the proposed framework is the relationship between regularization and linear dimensionality reduction. We show that the equivalent of the LDA or the QDA classifier in any linearly reduced subspace can be reached by using an appropriate regularization matrix. Furthermore, several such regularization matrices can be added together forming more complex regularizers. We utilize this framework to build regularization matrices that incorporate multiscale spectral representations. Several realizations of such regularization matrices are discussed, and their performances when applied to QDA classifiers are tested on four hyperspectral data sets. Often, the classifiers benefit from using the proposed regularization matrices.

Constrained log-likelihood-based semi-supervised linear discriminant analysis

A novel approach to semi-supervised learning for classical Fisher linear discriminant analysis is presented. It formulates the problem in terms of a constrained log-likelihood approach, where the semi-supervision comes in through the constraints. These constraints encode that the parameters in linear discriminant analysis fulfill particular relations involving label-dependent and label-independent quantities. In this way, the latter type of parameters, which can be estimated based on unlabeled data, impose constraints on the former. The former parameters are the class-conditional means and the average within-class covariance matrix, which are the parameters of interest in linear discriminant analysis. The constraints lead to a reduction in variability of the label-dependent estimates, resulting in a potential improvement of the semi-supervised linear discriminant over that of its regular supervised counterpart. We state upfront that some of the key insights in this contribution have been published previously in a workshop paper by the first author. The major contribution in this work is the basic observation that a semi-supervised linear discriminant analysis can be formulated in terms of a principled log-likelihood approach, where the previous solution employed an ad hoc procedure. With the current contribution, we move yet another step closer to a proper formulation of a semi-supervised version of this classical technique.