In Vitro and In Vivo Multispectral Photoacoustic Imaging for the Evaluation of Chromophore Concentration.

Multispectral photoacoustic imaging is a powerful noninvasive medical imaging technique that provides access to functional information. In this study, a set of methods is proposed and validated, with experimental multispectral photoacoustic images used to estimate the concentration of chromophores. The unmixing techniques used in this paper consist of two steps: (1) automatic extraction of the reference spectrum of each pure chromophore; and (2) abundance calculation of each pure chromophore from the estimated reference spectra. The compared strategies bring positivity and sum-to-one constraints, from the hyperspectral remote sensing field to multispectral photoacoustic, to evaluate chromophore concentration. Particularly, the study extracts the endmembers and compares the algorithms from the hyperspectral remote sensing domain and a dedicated algorithm for segmentation of multispectral photoacoustic data to this end. First, these strategies are tested with dilution and mixing of chromophores on colored 4% agar phantom data. Then, some preliminary in vivo experiments are performed. These consist of estimations of the oxygen saturation rate (sO2) in mouse tumors. This article proposes then a proof-of-concept of the interest to bring hyperspectral remote sensing algorithms to multispectral photoacoustic imaging for the estimation of chromophore concentration.

A Self-Supervised Deep Learning Approach for Blind Denoising and Waveform Coherence Enhancement in Distributed Acoustic Sensing Data.

Fiber-optic distributed acoustic sensing (DAS) is an emerging technology for vibration measurements with numerous applications in seismic signal analysis, including microseismicity detection, ambient noise tomography, earthquake source characterization, and active source seismology. Using laser-pulse techniques, DAS turns (commercial) fiber-optic cables into seismic arrays with a spatial sampling density of the order of meters and a time sampling rate up to one thousand Hertz. The versatility of DAS enables dense instrumentation of traditionally inaccessible domains, such as urban, glaciated, and submarine environments. This in turn opens up novel applications such as traffic density monitoring and maritime vessel tracking. However, these new environments also introduce new challenges in handling various types of recorded noise, impeding the application of traditional data analysis workflows. In order to tackle the challenges posed by noise, new denoising techniques need to be explored that are tailored to DAS. In this work, we propose a Deep Learning approach that leverages the spatial density of DAS measurements to remove spatially incoherent noise with unknown characteristics. This approach is entirely self-supervised, so no noise-free ground truth is required, and it makes no assumptions regarding the noise characteristics other than that it is spatio-temporally incoherent. We apply our approach to both synthetic and real-world DAS data to demonstrate its excellent performance, even when the signals of interest are well below the noise level. Our proposed methods can be readily incorporated into conventional data processing workflows to facilitate subsequent seismological analyses.

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.

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.

Nonlinear Unmixing of Hyperspectral Data With Vector-Valued Kernel Functions.

This paper presents a kernel-based nonlinear mixing model for hyperspectral data, where the nonlinear function belongs to a Hilbert space of vector valued functions. The proposed model extends the existing ones by accounting for band-dependent and neighboring nonlinear contributions. The key idea is to work under the assumption that nonlinear contributions are dominant in some parts of the spectrum, while they are less pronounced in other parts. In addition to this, we motivate the need for taking into account nonlinear contributions originating from the ground covers of neighboring pixels by practical considerations, precisely the adjacency effect. The relevance of the proposed model is that the nonlinear function is associated with a matrix valued kernel that allows to jointly model a wide range of nonlinearities and includes prior information regarding band dependences. Furthermore, the choice of the nonlinear function input allows to incorporate neighboring effects. The optimization problem is strictly convex and the corresponding iterative algorithm is based on the alternating direction method of multipliers. Finally, experiments conducted using synthetic and real data demonstrate the effectiveness of the proposed approach.

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

Mixing phenomena in hyperspectral images depend on a variety of factors, such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that the mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed detect-then-unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images.

Blind and fully constrained unmixing of hyperspectral images.

This paper addresses the problem of blind and fully constrained unmixing of hyperspectral images. Unmixing is performed without the use of any dictionary, and assumes that the number of constituent materials in the scene and their spectral signatures are unknown. The estimated abundances satisfy the desired sum-to-one and nonnegativity constraints. Two models with increasing complexity are developed to achieve this challenging task, depending on how noise interacts with hyperspectral data. The first one leads to a convex optimization problem and is solved with the alternating direction method of multipliers. The second one accounts for signal-dependent noise and is addressed with a reweighted least squares algorithm. Experiments on synthetic and real data demonstrate the effectiveness of our approach.

Nonlinear feature extraction using kernel principal component analysis with non-negative pre-image.

The inherent physical characteristics of many real-life phenomena, including biological and physiological aspects, require adapted nonlinear tools. Moreover, the additive nature in some situations involve solutions expressed as positive combinations of data. In this paper, we propose a nonlinear feature extraction method, with a non-negativity constraint. To this end, the kernel principal component analysis is considered to define the most relevant features in the reproducing kernel Hilbert space. These features are the nonlinear principal components with high-order correlations between input variables. A pre-image technique is required to get back to the input space. With a non-negative constraint, we show that one can solve the pre-image problem efficiently, using a simple iterative scheme. Furthermore, the constrained solution contributes to the stability of the algorithm. Experimental results on event-related potentials (ERP) illustrate the efficiency of the proposed method.