（1）Generalized Linear Mixing Model Accounting for Endmember Variability
（2）A Fast Multiscale Spatial Regularization for Sparse Hyperspectral Unmi
（3）Stochastic Analysis of Soft Limiters in the LMS Algorithm for Stationary White Gaussian Inputs - A Unified Theory
（4）A New Adaptive Video Super-Resolution Algorithm With Improved Robustness to Innovations
（5）A Design Methodology for the Gaussian KLMS Algorithm
报 告 人：Prof. Jose Carlos M. Bermudez
1)A New Adaptive Video Super-Resolution Algorithm With Improved Robustness to Innovations
Super-resolution reconstruction (SRR) is a well established approach for digital image quality improvement. SRR consists basically in combining multiple low-resolution (LR) images of the same scene or object in order to obtain one or more images of higher resolution (HR), outperforming physical limitations of image sensors. Video SRR algorithms often include a temporal regularization that constrains the norm of the changes in the solution between adjacent time instants. This introduces information about the correlation between adjacent frames, and tends to ensure video consistency over time, improving the quality of the reconstructed sequences. Although several techniques have led to considerable improvements in the quality of state of the art SRR algorithms, such improvements did not come for free. The computational cost of these algorithms is very high, which makes them unsuitable for real-time SRR applications. In particular, real-time video SRR applications require simple algorithms. The regularized least mean squares (R-LMS) is one notable example among the simpler SRR algorithms. Its quality in practical situations has been shown to be competitive even with that of costly and elaborated algorithms. Unfortunately, however, its performance is known to degrade severely in the presence of innovation outliers. This talk will describe a new adaptive video SRR algorithm with improved robustness to outliers when compared to the R-LMS algorithm. The algorithm is based on a new interpretation of the R-LMS update equation as the proximal regularization of the associated cost function, linearized about the previous estimate, which leads to a better understanding of its quality performance and robustness in different situations.
2) Generalized Linear Mixing Model Accounting for Endmember Variability
Hyperspectral imaging has attracted formidable interest of the scientific community in the past two decades, where hyperspectral images (HIs) have been explored in an increasing number of applications in different fields. The limited spatial resolution of hyperspectral devices often mixes the spectral contribution of different pure materials, termed endmembers, in the scene. This phenomenon is more prominent in remote sense applications due to the distance between airborne and spaceborne sensors and the target scene. The mixing process must be well understood to accurately unveil vital information relating the presence of pure materials and their distribution in the scene. Hyperspectral unmixing (HU) aims to solve this problem by decomposing the hyperspectral image (HI) into a collection of endmembers and their fractional abundances. Endmember variability is an important factor for accurately when 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 talk, we present a generalization of the ELMM that leads to a new model (GLMM) that is able to account for more complex spectral distortions, where different wavelength intervals can be affected unevenly. We also show how the existing methodology to jointly estimate the variability and the abundances can be extended for the GLMM.
3) Stochastic Analysis of Soft Limiters in the LMS Algorithm for Stationary White Gaussian Inputs - A Unified Theory
Saturation nonlinearities on the input and the error signal occur due to transducer or sensor limitations, or are introduced by the designer to increase algorithm robustness against outliers. This talk will show how the effects of saturation-type nonlinearities on the input and the error in the weight update equation for LMS adaptation can be investigated for a stationary white Gaussian data model for system identification. Nonlinear recursions are derived for the transient and steady-state weight first and second moments that include the effect of soft limiters on both the input and the error driving the algorithm. By varying a single parameter of the soft limiter, a general theory is presented that is applicable to LMS, soft limiting of the input, error or both, as well as the sign–sign LMS algorithm.
4) A Design Methodology for the Gaussian KLMS Algorithm
The Gaussian kernel least-mean-square (Gaussian KLMS) algorithm is the most popular adaptive algorithm for adaptive nonlinear system identification due to its simplicity and efficacy. The Gaussian KLMS has been studied under different implementation conditions. Though analytical models that predict its behavior are available, methodologies for determining the algorithm parameter values to satisfy prescribed design criteria are still missing in the literature. In this talk we will present a systematic methodology for the design of the Gaussian KLMS algorithm. Designing the algorithm consists in selecting adequate values for its free parameters from available theoretical performance models. These parameters comprise the filter length, the adaptive step-size, and the kernel bandwidth. The objective is to achieve specific design objectives, e.g., fast convergence time, good steady-state performance and/or reduced computational load. These goals are quantified in terms of different performance measures. Particularly, the time to convergence, the residual mean-squared-error (MSE), and the filter order.
5) Band Selection for Nonlinear Unmixing of Hyperspectral Images as a Maximal Clique Problem
The unmixing of spectral information acquired by hyperspectral sensors is at the core of many remote sensing applications such as land use analysis, mineral detection, environment monitoring and field surveillance. Such information is typically mixed at the pixel level due to the low resolution of hyperspectral devices or because distinct materials are combined into a homogeneous mixture. The observed reflectances then result from mixtures of several pure material signatures present in the scene, called endmembers. Considering that the endmembers have been identified, hyperspectral unmixing (HU) refers to estimating the proportional contribution of each endmember to each pixel in a scene. 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 talk will describe a centralized band selection (BS) method for supervised unmixing in the reproducing kernel Hilbert space (RKHS). 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 (MCP), i.e., searching for the biggest complete subgraph in a graph. Furthermore, we describe a strategy for selecting the coherence threshold and the Gaussian kernel bandwidth using coherence bounds for linearly independent bases.
6) A Fast Multiscale Spatial Regularization for Sparse Hyperspectral Unmixing
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 talk we will describe a novel multiscale spatial regularization approach for sparse unmixing. 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. 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.
报告人简介：José Carlos M. Bermudez received the B.E.E. degree from Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil, in 1978, the M.Sc. degree from COPPE/UFRJ, in 1981, and the Ph.D. degree from Concordia University, Montreal, Canada, in 1985, both in electrical engineering. He joined the Department of Electrical Engineering, Federal University of Santa Catarina (UFSC), Florianópolis, SC, Brazil, in 1985. He is currently a Professor of Electrical Engineering. He has been a visiting researcher for a number of times at the Concordia University, Montreal, Canada, at the University of Toulouse, France, and at University of Nice, France. He has spent one sabbatical year at the University of California Irvine in 1994 and one sabbatical year at the University of Toulouse in 2012.His research interests have involved analog signal processing using continuous-time and sampled-data systems. His recent research interests are in digital signal processing, including linear and nonlinear adaptive filtering, active noise and vibration control, echo cancellation, image processing, and hyperspectral imaging. Prof. Bermudez served as an Associate Editor of the IEEE TRANSACTIONS ON SIGNAL PROCESSING in the area of adaptive filtering from 1994 to 1996 and from 1999 to 2001. He was a member of the Signal Processing Theory and Methods Technical Committee of the IEEE Signal Processing Society from 1998 to 2004 and has been again a member of this committee from 2014 to the present. He is a Senior Area Editor for the IEEE TRANSACTIONS ON SIGNAL PROCESSING from July 2015 to the present. He is an IEEE Senior Member since 2002.