Nonparametric Detection of Nonlinearly Mixed Pixels and Endmember Estimation in Hyperspectral Images

Efficient TMS-Based Motor Cortex Mapping Using Gaussian Process Active Learning

Transcranial Magnetic Stimulation (TMS) can be used to map cortical motor topography by spatially sampling the sensorimotor cortex while recording Motor Evoked Potentials (MEP) with surface electromyography (EMG). Traditional sampling strategies are time-consuming and inefficient, as they ignore the fact that responsive sites are typically sparse and highly spatially correlated. An alternative approach, commonly employed when TMS mapping is used for presurgical planning, is to leverage the expertise of the coil operator to use MEPs elicited by previous stimuli as feedback to decide which loci to stimulate next. In this paper, we propose to automatically infer optimal future stimulus loci using active learning Gaussian Process-based sampling in place of user expertise. We first compare the user-guided (USRG) method to the traditional grid selection method and randomized sampling to verify that the USRG approach has superior performance. We then compare several novel active Gaussian Process (GP) strategies with the USRG approach. Experimental results using real data show that, as expected, the USRG method is superior to the grid and random approach in both time efficiency and MEP map accuracy. We also found that an active warped GP entropy and a GP random-based strategy performed equally as well as, or even better than, the USRG method. These methods were completely automatic, and succeeded in efficiently sampling the regions in which the MEP response variations are largely confined. This work provides the foundation for highly efficient, fully automatized TMS mapping, especially when considered in the context of advances in robotic coil operation.

Motor Cortex Mapping using Active Gaussian Processes

One important application of transcranial magnetic stimulation (TMS) is to map cortical motor topography by spatially sampling the motor cortex, and recording motor evoked potentials (MEP) with surface electromyography. Standard approaches to TMS mapping involve repetitive stimulations at different loci spaced on a (typically 1 cm) grid on the scalp. These mappings strategies are time consuming and responsive sites are typically sparse. Furthermore, the long time scale prevents measurement of transient cortical changes, and is poorly tolerated in clinical populations. An alternative approach involves using the TMS mapper expertise to exploit the map's sparsity through the use of feedback of MEPs to decide which loci to stimulate. In this investigation, we propose a novel active learning method to automatically infer optimal future stimulus loci in place of user expertise. Specifically, we propose an active Gaussian Process (GP) strategy with loci selection criteria such as entropy and mutual information (MI). The proposed method twists the usual entropy- and MI-based selection criteria by modeling the estimated MEP field, i.e., the GP mean, as a Gaussian random variable itself. By doing so, we include MEP amplitudes in the loci selection criteria which would be otherwise completely independent of the MEP values. Experimental results using real data shows that the proposed strategy can greatly outperform competing methods when the MEP variations are mostly conned in a sub-region of the space.

A Blind Multiscale Spatial Regularization Framework for Kernel-based Spectral Unmixing

Introducing spatial prior information in hyperspectral imaging (HSI) analysis has led to an overall improvement of the performance of many HSI methods applied for denoising, classification, and unmixing. Extending such methodologies to nonlinear settings is not always straightforward, specially for unmixing problems where the consideration of spatial relationships between neighboring pixels might comprise intricate interactions between their fractional abundances and nonlinear contributions. In this paper, we consider a multiscale regularization strategy for nonlinear spectral unmixing with kernels. The proposed methodology splits the unmixing problem into two sub-problems at two different spatial scales: a coarse scale containing low-dimensional structures, and the original fine scale. The coarse spatial domain is defined using superpixels that result from a multiscale transformation. Spectral unmixing is then formulated as the solution of quadratically constrained optimization problems, which are solved efficiently by exploring their strong duality and a reformulation of their dual cost functions in the form of root-finding problems. Furthermore, we employ a theory-based statistical framework to devise a consistent strategy to estimate all required parameters, including both the regularization parameters of the algorithm and the number of superpixels of the transformation, resulting in a truly blind (from the parameters setting perspective) unmixing method. Experimental results attest the superior performance of the proposed method when comparing with other, state-of-the-art, related strategies.

A Data Dependent Multiscale Model for Hyperspectral Unmixing With Spectral Variability

Spectral variability in hyperspectral images can result from factors including environmental, illumination, atmospheric and temporal changes. Its occurrence may lead to the propagation of significant estimation errors in the unmixing process. To address this issue, extended linear mixing models have been proposed which lead to large scale nonsmooth ill-posed inverse problems. Furthermore, the regularization strategies used to obtain meaningful results have introduced interdependencies among abundance solutions that further increase the complexity of the resulting optimization problem. In this paper we present a novel data dependent multiscale model for hyperspectral unmixing accounting for spectral variability. The new method incorporates spatial contextual information to the abundances in extended linear mixing models by using a multiscale transform based on superpixels. The proposed method results in a fast algorithm that solves the abundance estimation problem only once in each scale during each iteration. Simulation results using synthetic and real images compare the performances, both in accuracy and execution time, of the proposed algorithm and other state-of-the-art solutions.

Band Selection for Nonlinear Unmixing of Hyperspectral Images as a Maximal Clique Problem

Kernel-based nonlinear mixing models have been applied to unmix spectral information of hyperspectral images when the type of mixing occurring in the scene is too complex or unknown. Such methods, however, usually require the inversion of matrices of sizes equal to the number of spectral bands. Reducing the computational load of these methods remains a challenge in large-scale applications. This paper proposes a centralized band selection (BS) method for supervised unmixing in the reproducing kernel Hilbert space. It is based upon the coherence criterion, which sets the largest value allowed for correlations between the basis kernel functions characterizing the selected bands in the unmixing model. We show that the proposed BS approach is equivalent to solving a maximum clique problem, i.e., searching for the biggest complete subgraph in a graph. Furthermore, we devise a strategy for selecting the coherence threshold and the Gaussian kernel bandwidth using coherence bounds for linearly independent bases. Simulation results illustrate the efficiency of the proposed method.