Ricardo Augusto Borsoi

Ricardo Augusto Borsoi, Tales Imbiriba, Pau Closas

Multitemporal hyperspectral unmixing (MTHU) is a fundamental tool in the analysis of hyperspectral image sequences. It reveals the dynamical evolution of the materials (endmembers) and of their proportions (abundances) in a given scene. However, adequately accounting for the spatial and temporal variability of the endmembers in MTHU is challenging, and has not been fully addressed so far in unsupervised frameworks. In this work, we propose an unsupervised MTHU algorithm based on variational recurrent neural networks. First, a stochastic model is proposed to represent both the dynamical evolution of the endmembers and their abundances, as well as the mixing process. Moreover, a new model based on a low-dimensional parametrization is used to represent spatial and temporal endmember variability, significantly reducing the amount of variables to be estimated. We propose to formulate MTHU as a Bayesian inference problem. However, the solution to this problem does not have an analytical solution due to the nonlinearity and non-Gaussianity of the model. Thus, we propose a solution based on deep variational inference, in which the posterior distribution of the estimated abundances and endmembers is represented by using a combination of recurrent neural networks and a physically motivated model. The parameters of the model are learned using stochastic backpropagation. Experimental results show that the proposed method outperforms state of the art MTHU algorithms.

Ricardo Augusto Borsoi, Deniz Erdoğmuş, Tales Imbiriba

Although considerable effort has been dedicated to improving the solution to the hyperspectral unmixing problem, non-idealities such as complex radiation scattering and endmember variability negatively impact the performance of most existing algorithms and can be very challenging to address. Recently, deep learning-based frameworks have been explored for hyperspectral umixing due to their flexibility and powerful representation capabilities. However, such techniques either do not address the non-idealities of the unmixing problem, or rely on black-box models which are not interpretable. In this paper, we propose a new interpretable deep learning method for hyperspectral unmixing that accounts for nonlinearity and endmember variability. The proposed method leverages a probabilistic variational deep-learning framework, where disentanglement learning is employed to properly separate the abundances and endmembers. The model is learned end-to-end using stochastic backpropagation, and trained using a self-supervised strategy which leverages benefits from semi-supervised learning techniques. Furthermore, the model is carefully designed to provide a high degree of interpretability. This includes modeling the abundances as a Dirichlet distribution, the endmembers using low-dimensional deep latent variable representations, and using two-stream neural networks composed of additive piecewise-linear/nonlinear components. Experimental results on synthetic and real datasets illustrate the performance of the proposed method compared to state-of-the-art algorithms.

Luciano Carvalho Ayres, Sérgio José Melo de Almeida, José Carlos Moreira Bermudez et al.

Hyperspectral image (HI) analysis approaches have recently become increasingly complex and sophisticated. Recently, the combination of spectral-spatial information and superpixel techniques have addressed some hyperspectral data issues, such as the higher spatial variability of spectral signatures and dimensionality of the data. However, most existing superpixel approaches do not account for specific HI characteristics resulting from its high spectral dimension. In this work, we propose a multiscale superpixel method that is computationally efficient for processing hyperspectral data. The Simple Linear Iterative Clustering (SLIC) oversegmentation algorithm, on which the technique is based, has been extended hierarchically. Using a novel robust homogeneity testing, the proposed hierarchical approach leads to superpixels of variable sizes but with higher spectral homogeneity when compared to the classical SLIC segmentation. For validation, the proposed homogeneity-based hierarchical method was applied as a preprocessing step in the spectral unmixing and classification tasks carried out using, respectively, the Multiscale sparse Unmixing Algorithm (MUA) and the CNN-Enhanced Graph Convolutional Network (CEGCN) methods. Simulation results with both synthetic and real data show that the technique is competitive with state-of-the-art solutions.

Helena Calatrava, Ricardo Augusto Borsoi, Tales Imbiriba et al.

State inference and parameter learning in sequential models can be successfully performed with approximation techniques that maximize the evidence lower bound to the marginal log-likelihood of the data distribution. These methods may be referred to as Dynamical Variational Autoencoders, and our specific focus lies on the deep Kalman filter. It has been shown that the ELBO objective can oversimplify data representations, potentially compromising estimation quality. Tighter Monte Carlo objectives have been proposed in the literature to enhance generative modeling performance. For instance, the IWAE objective uses importance weights to reduce the variance of marginal log-likelihood estimates. In this paper, importance sampling is applied to the DKF framework for learning deep Markov models, resulting in the IW-DKF, which shows an improvement in terms of log-likelihood estimates and KL divergence between the variational distribution and the transition model. The framework using the sampled DKF update rule is also accommodated to address sequential state and parameter estimation when working with highly non-linear physics-based models. An experiment with the 3-space Lorenz attractor shows an enhanced generative modeling performance and also a decrease in RMSE when estimating the model parameters and latent states, indicating that tighter MCOs lead to improved state inference performance.

Ricardo Augusto Borsoi, Konstantin Usevich, David Brie et al.

Coupled tensor decompositions (CTDs) perform data fusion by linking factors from different datasets. Although many CTDs have been already proposed, current works do not address important challenges of data fusion, where: 1) the datasets are often heterogeneous, constituting different "views" of a given phenomena (multimodality); and 2) each dataset can contain personalized or dataset-specific information, constituting distinct factors that are not coupled with other datasets. In this work, we introduce a personalized CTD framework tackling these challenges. A flexible model is proposed where each dataset is represented as the sum of two components, one related to a common tensor through a multilinear measurement model, and another specific to each dataset. Both the common and distinct components are assumed to admit a polyadic decomposition. This generalizes several existing CTD models. We provide conditions for specific and generic uniqueness of the decomposition that are easy to interpret. These conditions employ uni-mode uniqueness of different individual datasets and properties of the measurement model. Two algorithms are proposed to compute the common and distinct components: a semi-algebraic one and a coordinate-descent optimization method. Experimental results illustrate the advantage of the proposed framework compared with the state of the art approaches.

Ashutosh Singh, Ricardo Augusto Borsoi, Deniz Erdogmus et al.

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based solutions face important challenges when dealing with spatio-temporal PDEs over long time scales. Specifically, the current theory of NOs does not present a systematic framework to perform data assimilation and efficiently correct the evolution of PDE solutions over time based on sparsely sampled noisy measurements. In this paper, we propose a learning-based state-space approach to compute the solution operators to infinite-dimensional semilinear PDEs. Exploiting the structure of semilinear PDEs and the theory of nonlinear observers in function spaces, we develop a flexible recursive method that allows for both prediction and data assimilation by combining prediction and correction operations. The proposed framework is capable of producing fast and accurate predictions over long time horizons, dealing with irregularly sampled noisy measurements to correct the solution, and benefits from the decoupling between the spatial and temporal dynamics of this class of PDEs. We show through experiments on the Kuramoto-Sivashinsky, Navier-Stokes and Korteweg-de Vries equations that the proposed model is robust to noise and can leverage arbitrary amounts of measurements to correct its prediction over a long time horizon with little computational overhead.

Luciano Carvalho Ayres, Ricardo Augusto Borsoi, José Carlos Moreira Bermudez et al.

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational complexity, and the solutions are very noise-sensitive. We generalize a multiscale spatial regularization approach to solve the unmixing problem by incorporating group sparsity-inducing mixed norms. Then, we propose a noise-robust method that can take advantage of the bundle structure to deal with endmember variability while ensuring inter- and intra-class sparsity in abundance estimation with reasonable computational cost. We also present a general heuristic to select the \emph{most representative} abundance estimation over multiple runs of the unmixing process, yielding a solution that is robust and highly reproducible. Experiments illustrate the robustness and consistency of the results when compared to related methods.

Haoqing Li, Ricardo Augusto Borsoi, Tales Imbiriba et al.

Autoencoder (AEC) networks have recently emerged as a promising approach to perform unsupervised hyperspectral unmixing (HU) by associating the latent representations with the abundances, the decoder with the mixing model and the encoder with its inverse. AECs are especially appealing for nonlinear HU since they lead to unsupervised and model-free algorithms. However, existing approaches fail to explore the fact that the encoder should invert the mixing process, which might reduce their robustness. In this paper, we propose a model-based AEC for nonlinear HU by considering the mixing model a nonlinear fluctuation over a linear mixture. Differently from previous works, we show that this restriction naturally imposes a particular structure to both the encoder and to the decoder networks. This introduces prior information in the AEC without reducing the flexibility of the mixing model. Simulations with synthetic and real data indicate that the proposed strategy improves nonlinear HU.

Ricardo Augusto Borsoi, Tales Imbiriba, Pau Closas et al.

The recent evolution of hyperspectral imaging technology and the proliferation of new emerging applications presses for the processing of multiple temporal hyperspectral images. In this work, we propose a novel spectral unmixing (SU) strategy using physically motivated parametric endmember representations to account for temporal spectral variability. By representing the multitemporal mixing process using a state-space formulation, we are able to exploit the Bayesian filtering machinery to estimate the endmember variability coefficients. Moreover, by assuming that the temporal variability of the abundances is small over short intervals, an efficient implementation of the expectation maximization (EM) algorithm is employed to estimate the abundances and the other model parameters. Simulation results indicate that the proposed strategy outperforms state-of-the-art multitemporal SU algorithms.

Ricardo Augusto Borsoi, Tales Imbiriba, José Carlos Moreira Bermudez et al.

Multiple Endmember Spectral Mixture Analysis (MESMA) is one of the leading approaches to perform spectral unmixing (SU) considering variability of the endmembers (EMs). It represents each EM in the image using libraries of spectral signatures acquired a priori. However, existing spectral libraries are often small and unable to properly capture the variability of each EM in practical scenes, which compromises the performance of MESMA. In this paper, we propose a library augmentation strategy to increase the diversity of existing spectral libraries, thus improving their ability to represent the materials in real images. First, we leverage the power of deep generative models to learn the statistical distribution of the EMs based on the spectral signatures available in the existing libraries. Afterwards, new samples can be drawn from the learned EM distributions and used to augment the spectral libraries, improving the overall quality of the SU process. Experimental results using synthetic and real data attest the superior performance of the proposed method even under library mismatch conditions.

Ricardo Augusto Borsoi

Video super-resolution reconstruction (SRR) algorithms attempt to reconstruct high-resolution (HR) video sequences from low-resolution observations. Although recent progress in video SRR has significantly improved the quality of the reconstructed HR sequences, it remains challenging to design SRR algorithms that achieve good quality and robustness at a small computational complexity, being thus suitable for online applications. In this paper, we propose a new adaptive video SRR algorithm that achieves state-of-the-art performance at a very small computational cost. Using a nonlinear cost function constructed considering characteristics of typical innovation outliers in natural image sequences and an edge-preserving regularization strategy, we achieve state-of-the-art reconstructed image quality and robustness. This cost function is optimized using a specific alternating projections strategy over non-convex sets that is able to converge in a very few iterations. An accurate and very efficient approximation for the projection operations is also obtained using tools from multidimensional multirate signal processing. This solves the slow convergence issue of stochastic gradient-based methods while keeping a small computational complexity. Simulation results with both synthetic and real image sequences show that the performance of the proposed algorithm is similar or better than state-of-the-art SRR algorithms, while requiring only a small fraction of their computational cost.

Ricardo Augusto Borsoi, Tales Imbiriba, José Carlos Moreira Bermudez et al.

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.

Ricardo Augusto Borsoi, Tales Imbiriba, José Carlos Moreira Bermudez

Endmember (EM) spectral variability can greatly impact the performance of standard hyperspectral image analysis algorithms. Extended parametric models have been successfully applied to account for the EM spectral variability. However, these models still lack the compromise between flexibility and low-dimensional representation that is necessary to properly explore the fact that spectral variability is often confined to a low-dimensional manifold in real scenes. In this paper we propose to learn a spectral variability model directly form the observed data, instead of imposing it \emph{a priori}. This is achieved through a deep generative EM model, which is estimated using a variational autoencoder (VAE). The encoder and decoder that compose the generative model are trained using pure pixel information extracted directly from the observed image, what allows for an unsupervised formulation. The proposed EM model is applied to the solution of a spectral unmixing problem, which we cast as an alternating nonlinear least-squares problem that is solved iteratively with respect to the abundances and to the low-dimensional representations of the EMs in the latent space of the deep generative model. Simulations using both synthetic and real data indicate that the proposed strategy can outperform the competing state-of-the-art algorithms.

Ricardo Augusto Borsoi, Tales Imbiriba, José Carlos Moreira Bermudez

Endmember (EM) variability has an important impact on the performance of hyperspectral image (HI) analysis algorithms. Recently, extended linear mixing models have been proposed to account for EM variability in the spectral unmixing (SU) problem. The direct use of these models has led to severely ill-posed optimization problems. Different regularization strategies have been considered to deal with this issue, but none so far has consistently exploited the information provided by the existence of multiple pure pixels often present in HIs. In this work, we propose to break the SU problem into a sequence of two problems. First, we use pure pixel information to estimate an interpolated tensor of scaling factors representing spectral variability. This is done by considering the spectral variability to be a smooth function over the HI and confining the energy of the scaling tensor to a low-rank structure. Afterwards, we solve a matrix-factorization problem to estimate the fractional abundances using the variability scaling factors estimated in the previous step, what leads to a significantly more well-posed problem. Simulation swith synthetic and real data attest the effectiveness of the proposed strategy.

Tales Imbiriba, Ricardo Augusto Borsoi, José Carlos Moreira Bermudez

Traditional hyperspectral unmixing methods neglect the underlying variability of spectral signatures often observed in typical hyperspectral images (HI), propagating these missmodeling errors throughout the whole unmixing process. Attempts to model material spectra as members of sets or as random variables tend to lead to severely ill-posed unmixing problems. Although parametric models have been proposed to overcome this drawback by handling endmember variability through generalizations of the mixing model, the success of these techniques depend on employing appropriate regularization strategies. Moreover, the existing approaches fail to adequately explore the natural multidimensinal representation of HIs. Recently, tensor-based strategies considered low-rank decompositions of hyperspectral images as an alternative to impose low-dimensional structures on the solutions of standard and multitemporal unmixing problems. These strategies, however, present two main drawbacks: 1) they confine the solutions to low-rank tensors, which often cannot represent the complexity of real-world scenarios; and 2) they lack guarantees that endmembers and abundances will be correctly factorized in their respective tensors. In this work, we propose a more flexible approach, called ULTRA-V, that imposes low-rank structures through regularizations whose strictness is controlled by scalar parameters. Simulations attest the superior accuracy of the method when compared with state-of-the-art unmixing algorithms that account for spectral variability.

Ricardo Augusto Borsoi, Tales Imbiriba, José Carlos Moreira Bermudez

Image fusion combines data from different heterogeneous sources to obtain more precise information about an underlying scene. Hyperspectral-multispectral (HS-MS) image fusion is currently attracting great interest in remote sensing since it allows the generation of high spatial resolution HS images, circumventing the main limitation of this imaging modality. Existing HS-MS fusion algorithms, however, neglect the spectral variability often existing between images acquired at different time instants. This time difference causes variations in spectral signatures of the underlying constituent materials due to different acquisition and seasonal conditions. This paper introduces a novel HS-MS image fusion strategy that combines an unmixing-based formulation with an explicit parametric model for typical spectral variability between the two images. Simulations with synthetic and real data show that the proposed strategy leads to a significant performance improvement under spectral variability and state-of-the-art performance otherwise.

Ricardo Augusto Borsoi, Tales Imbiriba, José Carlos Moreira Bermudez

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.

Tales Imbiriba, Ricardo Augusto Borsoi, José Carlos Moreira Bermudez

Tensor-based methods have recently emerged as a more natural and effective formulation to address many problems in hyperspectral imaging. In hyperspectral unmixing (HU), low-rank constraints on the abundance maps have been shown to act as a regularization which adequately accounts for the multidimensional structure of the underlying signal. However, imposing a strict low-rank constraint for the abundance maps does not seem to be adequate, as important information that may be required to represent fine scale abundance behavior may be discarded. This paper introduces a new low-rank tensor regularization that adequately captures the low-rank structure underlying the abundance maps without hindering the flexibility of the solution. Simulation results with synthetic and real data show that the the extra flexibility introduced by the proposed regularization significantly improves the unmixing results.

Ricardo Augusto Borsoi, Tales Imbiriba, José Carlos Moreira Bermudez et al.

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit from spatial regularization strategies. While existing spatial regularization methods improve the problem conditioning and promote piecewise smooth solutions, they lead to large nonsmooth optimization problems. Thus, efficiently introducing spatial context in the unmixing problem remains a challenge, and a necessity for many real world applications. In this paper, a novel multiscale spatial regularization approach for sparse unmixing is proposed. The method uses a signal-adaptive spatial multiscale decomposition based on superpixels to decompose the unmixing problem into two simpler problems, one in the approximation domain and another in the original domain. Simulation results using both synthetic and real data indicate that the proposed method can outperform state-of-the-art Total Variation-based algorithms with a computation time comparable to that of their unregularized counterparts.

Tales Imbiriba, Ricardo Augusto Borsoi, José Carlos Moreira Bermudez

Endmember variability is an important factor for accurately unveiling vital information relating the pure materials and their distribution in hyperspectral images. Recently, the extended linear mixing model (ELMM) has been proposed as a modification of the linear mixing model (LMM) to consider endmember variability effects resulting mainly from illumination changes. In this paper, we further generalize the ELMM leading to a new model (GLMM) to account for more complex spectral distortions where different wavelength intervals can be affected unevenly. We also extend the existing methodology to jointly estimate the variability and the abundances for the GLMM. Simulations with real and synthetic data show that the unmixing process can benefit from the extra flexibility introduced by the GLMM.

Ricardo Augusto Borsoi, Guilherme Holsbach Costa, José Carlos Moreira Bermudez

In this paper, a new video super-resolution reconstruction (SRR) method with improved robustness to outliers is proposed. Although the R-LMS is one of the SRR algorithms with the best reconstruction quality for its computational cost, and is naturally robust to registration inaccuracies, its performance is known to degrade severely in the presence of innovation outliers. By studying the proximal point cost function representation of the R-LMS iterative equation, a better understanding of its performance under different situations is attained. Using statistical properties of typical innovation outliers, a new cost function is then proposed and two new algorithms are derived, which present improved robustness to outliers while maintaining computational costs comparable to that of R-LMS. Monte Carlo simulation results illustrate that the proposed method outperforms the traditional and regularized versions of LMS, and is competitive with state-of-the-art SRR methods at a much smaller computational cost.