J.C.M. Bermudez

Karoline da Rocha, José C. M. Bermudez, Elena R. C. Rivero et al.

The Epithelial Dysplasia (ED) is a tissue alteration commonly present in lesions preceding oral cancer, being its presence one of the most important factors in the progression toward carcinoma. This study proposes a method to design a low computational cost classification system to support the detection of dysplastic epithelia, contributing to reduce the variability of pathologist assessments. We employ a multilayer artificial neural network (MLP-ANN) and defining the regions of the epithelium to be assessed based on the knowledge of the pathologist. The performance of the proposed solution was statistically evaluated. The implemented MLP-ANN presented an average accuracy of 87%, with a variability much inferior to that obtained from three trained evaluators. Moreover, the proposed solution led to results which are very close to those obtained using a convolutional neural network (CNN) implemented by transfer learning, with 100 times less computational complexity. In conclusion, our results show that a simple neural network structure can lead to a performance equivalent to that of much more complex structures, which are routinely used in the literature.

Celso H. H. Ribas, José C. M. Bermudez

Access to data and data processing, including the use of machine learning techniques, has become significantly easier and cheaper in recent years. Nevertheless, solutions that can be widely adopted by regulators for market monitoring and inspection targeting in a data-driven way have not been frequently discussed by the scientific community. This article discusses the need and the difficulties for the development of such solutions, presents an effective method to address regulation planning, and illustrates its use to account for the most important and common subject for the majority of regulators: the consumer. This article hopes to contribute to increase the awareness of the regulatory community to the need for data processing methods that are objective, impartial, transparent, explainable, simple to implement and with low computational cost, aiming to the implementation of risk-based regulation in the world.

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.

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, 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) 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 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.

Ricardo A. Borsoi, Julio C. C. Aya, Guilherme H. Costa et al.

Electrical Impedance Tomography (EIT) systems are becoming popular because they present several advantages over competing systems. However, EIT leads to images with very low resolution. Moreover, the nonuniform sampling characteristic of EIT precludes the straightforward application of traditional image ruper-resolution techniques. In this work, we propose a resampling based Super-Resolution method for EIT image quality improvement. Preliminary results show that the proposed technique can lead to substantial improvements in EIT image resolution, making it more competitive with other technologies.

Jingen Ni, Jian Yang, Jie Chen et al.

Some system identification problems impose nonnegativity constraints on the parameters to estimate due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow to address this problem in an online manner. A nonnegative least mean fourth (NNLMF) algorithm has been recently proposed to improve the performance of these algorithms in cases where the measurement noise is not Gaussian. This paper provides a first theoretical analysis of the stochastic behavior of the NNLMF algorithm for stationary Gaussian inputs and slow learning. Simulation results illustrate the accuracy of the proposed analysis.

Tales Imbiriba, José Carlos Moreira Bermudez, Cédric Richard et al.

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 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.

T. Imbiriba, J. C. M. Bermudez, C. Richard et al.

The profusion of spectral bands generated by the acquisition process of hyperspectral images generally leads to high computational costs. Such difficulties arise in particular with nonlinear unmixing methods, which are naturally more complex than linear ones. This complexity, associated with the high redundancy of information within the complete set of bands, make the search of band selection algorithms relevant. With this work, we propose a band selection strategy in reproducing kernel Hilbert spaces that allows to drastically reduce the processing time required by nonlinear unmixing techniques. Simulation results show a complexity reduction of two orders of magnitude without compromising unmixing performance.

Jie Chen, Wei Gao, Cédric Richard et al.

The kernel least-mean-square (KLMS) algorithm is an appealing tool for online identification of nonlinear systems due to its simplicity and robustness. In addition to choosing a reproducing kernel and setting filter parameters, designing a KLMS adaptive filter requires to select a so-called dictionary in order to get a finite-order model. This dictionary has a significant impact on performance, and requires careful consideration. Theoretical analysis of KLMS as a function of dictionary setting has rarely, if ever, been addressed in the literature. In an analysis previously published by the authors, the dictionary elements were assumed to be governed by the same probability density function of the input data. In this paper, we modify this study by considering the dictionary as part of the filter parameters to be set. This theoretical analysis paves the way for future investigations on KLMS dictionary design.