IEEE Geoscience and Remote Sensing Magazine - June 2013 - 26

to their nonlinear versions [133], [154] by using the ideas in
kernel machine learning theory. Experimental results show
that typically the kernel-based algorithms outperform their
linear versions.

1
0.9
Probability of Detection

0.8
0.7
0.6
0.5
0.4

Sparsity−Based with Smooting
Sparsity−Based Without Smoothing
SVM−CK
MSD
SMF
ASD

0.3
0.2
0.1
0

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
False Alarm Rate

1

FIGURE 13. ROC curves for a typical hyperspectral image (FR-I)
with several military targets reproduced from [152].

signature-based target detection techniques, the experimental detail and results for couple of other hyperspectral
images can be found in [152].
D. nonlineAR DetectoRs
Almost all the anomaly and target detectors are based on
only exploiting first and second order statistics in order
to identify anomalies or targets. Kernel machine learning
theory [132] has emerged as a new nonlinear-based learning approach for extending the classical pattern recognition
algorithms. The implicit exploitation of nonlinear features
through kernels provides crucial information about a given
dataset which, in general, the learning methods based on
linear models cannot achieve. The RX anomaly detection
algorithm, the statistical target detection algorithms and
the sparsity-based target classifier have all been extended

Additional
Variables
Radiative
Transfer
Variables
of Interest

Inverse
Problem

Observation
Configuration

Forward
Problem

Remote
Sensing
Data

Retrieval
Algorithm
Prior
Knowledge

e. chAllenges
The major challenges in the classical anomaly and target
detection techniques (RX, SMF, MSD, ASD, OSP) are still
the need for developing new approaches for estimating the
background/target covariance matrices or their corresponding subspaces given a limited training data. Further research
is also needed in the classical techniques to incorporate the
spatial-contextual information about the targets that are
more than one pixel size. In the case of sparsity-based techniques more research is needed to develop the appropriate
class sub-dictionaries as well as compact discriminative
dictionaries. More advanced structured sparsity priors are
to be incorporated and their performance evaluated. Currently most of the non-linear methods are based on kernel
learning theory, other nonlinear approaches beside kernelbased methods need to be introduced.
vI. EstImatIon oF lanD pHysIcal paRamEtERs
This section reviews the main problems and methods in
the field of model inversion and estimation of physical
parameters. Our main goal in remote sensing is to monitor
the Earth and its interaction with the atmosphere. The
analysis can be done at local or global scales by looking at
bio-geo-chemical cycles, atmospheric state and evolution,
and vegetation dynamics [155], [156]. All these complex interactions can be studied through the definition of
physical parameters representing different properties for
land (e.g., surface temperature, biomass, leaf area coverage),
water (e.g., yellow substance, ocean color, suspended matter)
or the atmosphere (e.g., temperature and moisture profiles at different altitudes). The field of physical parameter
estimation is an intermediate modeling step necessary to
transform the measurements13 into useful estimates [157].
The remote sensing modeling system is illustrated in
Fig. 14. The forward (or direct) problem involves radiative
transfer models (RTMs). These models summarize the physical processes involved in the energy transfer from canopies
and atmosphere to measured radiance. They simulate the
reflected or emitted radiation transmitted through the
atmosphere for a given observation configuration (e.g.,
wavelength, view and illumination directions) and some
auxiliary variables (e.g., vegetation and atmosphere characteristics). Solving the inversion problem implies the design
of algorithms that, starting from the radiation acquired by
the sensor, can give accurate estimates of the variables of
interest, thus "inverting" the RTM. In the inversion process,
a priori information of the variables of interest can also be
13

FIGURE 14. Forward (solid lines) and inverse (dashed lines)

problems in remote sensing. Figure adapted from [157].
26

The acquired data may consist of multispectral or hyperspectral images
provided by satellite or airborne sensors, but can also integrate spectra acquired by in situ (field) radiometers, GIS data that help to integrate geographical information, or radiosonde measures for weather monitoring.
ieee Geoscience and remote sensinG maGazine

june 2013



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