IEEE Geoscience and Remote Sensing Magazine - June 2016 - 25
visible units v = {0, 1} D and hidden units h = {0, 1} F . A
joint configuration of the units has an energy given by
E (v, h: i) = -
D
F
D
i= 1
j= 1
F
/ b i v i - / a j h j - / / w i v i h j,
(7)
i= 1 j= 1
where i = {b i, a j, w ij} and wij is the weight between visible
unit i and hidden unit j, and bi and aj are bias terms of the
visible and hidden unit, respectively.
The joint distribution over the units is defined by
P (v, h: i) =
Z (i) =
1 -E (v, h: i)
e
Z (i)
(8)
/ / E (v, h: i),
(9)
v
h
where Z ^i h is the normalizing constant. The network assigns a probability to every input vector via the energy function. The probability of the training vector can be raised by
adjustment to lower the energy, as given in (7). The conditional distributions of hidden unit h and input vector v are
given by the logistic function
D
p (h j = 1|v) = g d / W ij v i + a j n ,
(10)
i=1
F
p (v j = 1|h) = g e / W ij h i + b j o ,
(11)
j=1
g (x) =
1
.
1 + e (- x)
(12)
Once the states of hidden units are chosen, the input data
can be reconstructed by setting each vi to 1 with the probability in (11). The hidden units' states are then updated to
represent the features of the reconstruction. The learning of
W is done through a method called contrastive divergence (CD).
The DBN has been applied to the RS image spatial-spectral
classification and shows superior performance compared to
the conventional feature dimensionality-reduction methods,
such as principal component analysis (PCA), and classifiers,
such as support vector machines (SVMs) [55], [29]. In recent
years, it has also been successfully proposed for object recognition [56] and scene classification [57].
sParse CodinG
Sparse coding is a type of unsupervised method for learning sets of overcomplete bases to represent data efficiently to
find a set of basis vectors z i such that we can represent an
input vector x as a linear combination of these basis vectors:
x=
k
/ ai zi .
(13)
i= 1
While techniques such as PCA allow us to learn a complete
set of basis vectors efficiently, we wish to learn an overcomplete set of basis vectors to represent the input vectors x. The
advantage of having an overcomplete basis set is that our basis vectors are better able to capture structures and patterns
inherent in the input data. However, with an overcomplete
26
basis set, the coefficients ai are no longer uniquely determined by the input vector x. Therefore, in sparse coding, we
introduce the additional criterion of sparsity to resolve the
degeneracy introduced by the overcompleteness.
We define the sparse coding cost function on a set of m
input vectors as
m
min / x j a, z
j= 1
k
2
i= 1
2
/ a ij z i
k
+ m / S (a i ) ,
j
(14)
i= 1
where S ^ $ h is a sparsity cost function that penalizes ai for
being far from zero. We can interpret the first term of the
sparse coding objective as a reconstruction term that tries
to force the algorithm to provide a good representation of
x, and the second term can be defined as a sparsity penalty
that forces our representation of x to be sparse.
A large number of sparse coding methods have been proposed. Notably, for RS scene classification, Cheriyadat [58]
introduces a variant of sparse coding that combines local
scale-invariant feature transform (SIFT)-based feature descriptors to generate a new sparse representation, while, in
[59], the sparse coding is used to reduce the potential redundant information in the feature representation. In addition,
as a computationally efficient unsupervised feature-learning technique, k-means clustering has also been played as
a single-layer feature extractor for RS scene classification
[60]-[62] and achieves state-of-the-art performance.
deeP LeARnIng foR ReMote sensIng dAtA
The "Basic Algorithms in Deep Learning" section discussed
some of the basic elements used in constructing a DL architecture as well as the general framework. In practice,
the mathematical problems of the various RS data analysis
techniques can be regarded as special cases of input-output
data combined with a particular DL network based on the
aforementioned algorithms. In this section, we provide a
tutorial on DL for RS data from four perspectives: 1) image
preprocessing, 2) pixel-based classification, 3) target recognition, and 4) scene understanding.
remote sensinG imaGe PreProCessinG
In practice, the observed RS images are not always as satisfactory as we demand due to many factors, including the
limitations of the sensors and the influence of the atmosphere. Therefore, there is a need for RS image preprocessing to enhance the image quality before the subsequent
classification and recognition tasks. According to the related RS literature, most of the existing methods in RS image
denoising, deblurring, superresolution, and pan sharpening are based on the standard image-processing techniques
in the signal processing society, while there are very few
machine-learning-based techniques. In fact, if we can effectively model the intrinsic correlation between the input
(observed data) and output (ideal data) by a set of training
samples, then the observed RS image could be enhanced
by the same model. According to the basic techniques in
the previous section, such an intrinsic correlation can be
ieee Geoscience and remote sensing magazine
june 2016
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