Poster Session and Reception
Tuesday, September 24, 2013 - 4:45pm - 6:00pm
- A Method for Finding Structured Sparse Solutions to Non-negative Least Squares Problems with Applications
Yifei Lou (University of California)
Demixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require ﬁnding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how aspects of these problems, such as misalignment of DOAS references and uncertainty in hyperspectral endmembers, can be modeled by expanding the dictionary with grouped elements and imposing a structured sparsity assumption that the combinations within each group should be sparse or even 1-sparse. If the dictionary is highly coherent, it is difficult to obtain good solutions using convex or greedy methods, such as non-negative least squares (NNLS) or orthogonal matching pursuit. We use penalties related to the Hoyer measure, which is the ratio of the l1 and l2 norms, as sparsity penalties to be added to the objective in NNLS-type models. For solving the resulting nonconvex models, we propose a scaled gradient projection algorithm that requires solving a sequence of strongly convex quadratic programs. We discuss its close connections to convex splitting methods and difference of convex programming. We also present promising numerical results for example DOAS analysis and hyperspectral demixing problems.
- Sparse SVMs for Hyperspectral Band Selection
Sofya Chepushtanova (Colorado State University)
We explore sparse support vector machines (SSVMs) for the hyperspectral imagery band selection problem. An SSVM has a 1-norm regularizer in the objective function which suppresses many components of w, the normal vector to the separating hyperplane between two classes of data, and thus indicates spectral bands that are effective at separating the data. We propose a band selection framework in which we use the effectiveness and sparsity of SSVMs combined with bootstrap aggregation approach to reduce variability in the components of w and find the redundant bands.We can eliminate more bands by reapplying SSVMs to the reduced data and cutting off the bandsbased on comparing magnitude ratios throughout the list of the ranked bands. We propose to extend a binary band selection to a multiclass case by using one-against-one (OAO) SSVMs and different methods of band ranking all over the multiple classes to find a superset of relevant bands. At the last step of the method, spatial smoothing by majority filter is used to improve the classification results. We illustrate the perfomance of the method on the AVIRIS Indian Pines data set with high accuracy rates achieved on different subsets of selected bands.
- Characterizing Spatial and Temporal Evolution of Soil Surface Roughness
Antonio Paz González (Universidade da Coruña)
Spatially distributed information on soil microtopography is required for a better understanding
of several processes in hydrology, geomorphology and soil sciences. The objectives of this study were:
i) to compare several statistical, geostatistical and fractal indices used to describe soil surface roughness and
ii) to show how these indices can quantify the space and time evolution of the highly heterogeneous soil
structure following water erosion and runoff. The microtopography of the soil surface was digitized by
an instantaneous profile laser scanner before and after application of simulated rainfall at a 2 mm resolution.
The roughness indices calculated included random roughness (statistical), sill and range of the semivariogram
(geostatistical), fractal dimension and fractal length (fractal) and various parameters gathered from generalized
dimension and singularity spectra (multifractal). These indices were interpreted in the context of aggregate
breakdown and soil surface crusting. The performance of the various mathematical tools employed to describe
either the vertical or the spatial components of the soil surface roughness was shown to be different.
The suitability of this indices for inclusion as spatial information in hydrology and erosion models is
also an important aspect to be considered.
Joint work with: Eva Vidal Vázquez and Ildegardis Bertol
- Shape and Pose Recovery of Solar-Illuminated Surfaces from Compressive Spectral-Polarimetric Image Data
Peter Zhang (Wake Forest Medical School)
We present simulation-based studies of the use of compressively
sensed spectral-polarimetric spatial image data from a solar-illuminated
reflecting surface to recover its material signature,
three-dimensional (3D) shape, pose, and degree of surface
roughness. The spatial variations of the polarimetric Bidirectional
Reflectance Distribution Function (pBRDF) around glint points
contain unique information about the shape and roughness of the
reflecting surface that is revealed most dramatically in
polarization-difference maps from which the spatially generalized
diffuse-scattering contributions to brightness are largely absent.
Here we employ a specific compressed-sensing protocol, the socalled
Coded-Aperture Snapshot Spectral-Polarimetric Imager
(CASSPI) advanced recently by Tsai and Brady, to simulate noisy
measurements from which these surface attributes are recovered
robustly in a sequential manner.
Joint work with Sudhakar Prasad and Robert J. Plemmons.
- Unmixing Analysis Based on Multiscale Representation
Miguel Velez-Reyes (University of Texas)
The measured spectral signature in the field of view of a remote sensor rarely comes from a single material. Unmixing refers to the extraction of the number, the spectral signature, and the abundance of the materials or endmembers in the field of view of the sensor. Unmixing plays an important role in hyperspectral image processing in a wide range of application. Most unmixing techniques are pixel–based procedures that do not take advantage of spatial information provided by the hyperspectral image. Here we present an approach for unmixing of hyperspectral imagery based on a spatial multiscale representation which allows the identification of locally spectrally uniform areas that are used as candidate endmembers. Extracted signatures are clustered into endmember classes that account for the spectral variability of endmembers. Abundances are estimated using constrained least square methods. Experimental results using AVIRIS imagery are presented to demonstrate the proposed approach.