Andrea Marinoni

A Novel Approach for Efficient

Airborne and spaceborne hyperspectral sensors, due to their limited spatial resolution, often record the spectral response of a mixture of materials. In order to extract the abundances of these materials, linear and nonlinear unmixing algorithms have been developed. In this paper, we focus on nonlinear mixing models that are able to model macro- and microscopic scale interactions. Although very useful, these models may be inverted only by means of optimization techniques, typically impossible to be performed in matrix form. Thereby, only nonlinear mixing models that describe macroscopic effects (e.g., two-reflections schemes) are currently considered as they have lower computational costs. On the other hand, this limitation may result in a loss in terms of description accuracy for the images. In this paper, we propose a new approach for nonlinear unmixing that aims at providing excellent reconstruction performance for arbitrary polynomial nonlinearities making use of the polytope decomposition (POD) method. Additionally, POD transforms nonlinear unmixing into a linear problem, and can be easily implemented in high-performance computing architectures. Results using synthetic and real data confirm the effectiveness and accuracy of the proposed framework. To prove its feasibility for fast computational applications, its complexity is analytically derived and compared with real data analysis.

p

Nonlinear hyperspectral unmixing (HSU) plays a key-role in understanding and quantifying the physical-chemical phenomena occurring over geometrically complex fields of view. Nonlinear HSU methods that do not rely on prior knowledge of the ground truth to analyze the scene are especially interesting. However, they can be affected either by overfitting or performance degradation provided by inaccurate setting of unmixing parameters. In this paper, we introduce a new nonlinear HSU architecture which aims at taking advantage of the benefit provided by the combination of polytope decomposition (POD) method together with artificial neural network (ANN)-based learning. Specifically, ANN is able to efficiently estimate the order p of the nonlinearity provided by the given scene even without the thorough knowledge of the ground truth. The ANN-based learning is used to feed the POD in order to deliver accurate unmixing based on a p-linear polynomial model. Experimental results over simulated and real scenes show promising performance of the proposed framework.

-Linear Hyperspectral Unmixing

This paper introduces a protograph-based method for designing q-ary LDPC codes for use with modulations larger than QPSK. Simulations focus on a GF(16), 16-QAM example. The proposed construction method achieves the maximum gain when the average column weight is chosen so that the linear minimum distance growth property is satisfied. In this region, the benefit of a protograph-based design over a standard PEG approach was 0.3 dB. We found that a careful field-element selection algorithm provides about 0.1 dB of improvement over random field-element selection. Overall, the proposed improvements yielded 0.4 dB of gain over a PEG-based GF(16) code with randomly selected Galois field elements. The performance of this baseline GF(16) code was comparable to the best known binary LDPC code for 16-QAM, so that the proposed improvements allow the GF(16) LDPC code to outperform known binary approaches.

Nonlinear Hyperspectral Unmixing Using Nonlinearity Order Estimation and Polytope Decomposition

In this work we consider an optimized design of q-ary low-density parity-check (LDPC) codes that takes into account their burst error correction capability. In recent works, the performance of LDPC decoding in presence of noise bursts has been related to the structure of the parity-check matrix. In particular, two approaches to characterize the burst error correction capabilities have been proposed in the literature. Following these ideas, we compare different matrix designs in order to choose the best matrix constraints to be maximized in a PEG construction. Several non-binary LDPC codes, generated with the proposed design methods are compared. Their performance are analyzed in the context of magnetic recording channels, where they are considered a promising alternative to the Reed Solomon (RS) codes.

Protograph-based q-ary LDPC codes for higher-order modulation

Higher order nonlinear material mixtures provide a good model to explain the effects of physical-chemical phenomena on hyperspectral remote sensing measurements. Therefore, inverting nonlinear effects starting from the measured spectral values is a very challenging yet fundamental task to provide a thorough and reliable characterization of the materials in a scene. In this paper, this task is achieved by inverting a new model for nonlinear hyperspectral mixtures. Specifically, we show that it is possible to effectively unmix hyperspectral data by assuming a harmonic description of the higher order nonlinear combination of the endmembers. The rationale for this model is that the harmonic analysis is able to understand and quantify effects that cannot be effectively described by classic polynomial combinations. Although the model is nonlinear, unmixing is performed by solving a linear system thanks to the recently proposed polytope decomposition (POD). Experimental results show that inverting this model leads to improved performances with respect to the state of the art in terms of endmember abundance estimation both over synthetic and real datasets.

Efficient design of non-binary LDPC codes for magnetic recording channels, robust to error bursts

This work provides a novel approach to non-linear unmixing of hyperspectral images assuming a polynomial postnonlinear mixing model. The new model exploits polytope decomposition to compute abundances under a polynomial approximation which is computed on a pixel by pixel basis in a very efficient way, with no requirements for a global optimization for the whole scene. The approach is validated with artificial and actual scenes and shows improvements over similar state of the art techniques.

Harmonic Mixture Modeling for Efficient Nonlinear Hyperspectral Unmixing

A very interesting perspective of “big data” in diabetes management stands in the integration of environmental information with data gathered for clinical and administrative purposes, to increase the capability of understanding spatial and temporal patterns of diseases. Within the MOSAIC project, funded by the European Union with the goal to design new diabetes analytics, we have jointly analyzed a clinical-administrative dataset of nearly 1.000 type 2 diabetes patients with environmental information derived from air quality maps acquired from remote sensing (satellite) data. Within this context we have adopted a general analysis framework able to deal with a large variety of temporal, geo-localized data. Thanks to the exploitation of time series analysis and satellite images processing, we studied whether glycemic control showed seasonal variations and if they have a spatiotemporal correlation with air pollution maps. We observed a link between the seasonal trends of glycated hemoglobin and air pollution in some of the considered geographic areas. Such findings will need future investigations for further confirmation. This work shows that it is possible to successfully deal with big data by implementing new analytics and how their exploration may provide new scenarios to better understand clinical phenomena.

Non-linear hyperspectral unmixing by polytope decomposition

In order to achieve a better knowledge of the effect of the anthropogenic extents over the environment, extracting reliable and effective information by Earth observations (EOs) is crucial to help developing a sound human-environment interaction (HEI) assessment. In this sense, the use of future hyperspectral sensors for wide area characterization leads to the need of hyperspectral unmixing (HSU) architectures to recognize urban materials and structures. Further, as urban settlements are often characterized by geometrically and spectrally complex scenarios, the nonlinear reflectance interplay among the elements that constitute each scene must be very well detailed and described so that a thorough knowledge of the scenes can be carried out. In this paper, properly set higher order nonlinear mixture models are used to perform an accurate characterization of the anthropogenic settlements in several EO scenes acquired in different continents. Moreover, a brand new index for estimation of urban extents is provided. Experimental results show how the proposed approach is able to deliver accurate and reliable characterization of urban materials and extents.

Integration of Administrative, Clinical, and Environmental Data to Support the Management of Type 2 Diabetes Mellitus: From Satellites to Clinical Care.

Recently q-ary Low-Density Parity-Check (LDPC) codes have been used to achieve performance close to the channel capacity in different channel environments, from satellite communications to magnetic data storage systems. Design of receivers employing these codes for transmissions over channels affected by InterSymbol Interference (ISI) is still an open issue. In fact, detection-and-decoding systems have to face the trade-off between error-rate performance and complexity. In this paper we compare some receiver architectures for 16-ary LDPC codes: serial and turbo concatenated schemes and a joint Message-Passing (MP) based receiver as well. Performance of these systems are evaluated over three different Partial Response (PR) channels, using simulations. Finally, ongoing future directions for research are discussed.

Accurate Detection of Anthropogenic Settlements in Hyperspectral Images by Higher Order Nonlinear Unmixing

Spectral unmixing is an important technique for exploiting hyperspectral data. The presence of nonlinear mixing effects poses an important problem when attempting to provide accurate estimates of the abundance fractions of pure spectral components (endmembers) in a scene. This problem complicates the development of algorithms that can address all types of nonlinear mixtures in the scene. In this paper, we develop a new strategy to simultaneously estimate both the endmember signatures and their corresponding abundances using a biswarm particle swarm optimization (BiPSO) bilinear unmixing technique based on Fans model. Our main motivation in this paper is to explore the potential of the newly proposed bilinear mixture model based on particle swarm optimization (PSO) for nonlinear spectral unmixing purposes. By taking advantage of the learning mechanism provided by PSO, we embed a multiobjective optimization technique into the algorithm to handle the more complex constraints in simplex volume minimization algorithms for spectral unmixing, thus avoiding limitations due to penalty factors. Our experimental results, conducted using both synthetic and real hyperspectral data, demonstrate that the proposed BiPSO algorithm can outperform other traditional spectral unmixing techniques by accounting for nonlinearities in the mixtures present in the scene.