A hierarchical
recognition system (HRS) based on constrained Deep Belief Network
(DBN) is proposed for SAR Automatic Target Recognition (SAR ATR). As
a classical Deep Learning method, DBN has shown great
performance on data reconstruction, big data mining, and
classification. However, few works have been carried out to solve
small data problems (like SAR ATR) by Deep Learning method. In HRS,
the deep structure and pattern classifier are combined to solve small
data classification problems. After building the DBN with multiple
Restricted Boltzmann Machines (RBMs), hierarchical features can be
obtained, and then they are fed to classifier directly. To obtain more
natural sparse feature representation, the Constrained RBM (CRBM) is
proposed with solving a generalized optimization problem. Three RBM
variants,
Synthetic Aperture Radar (SAR) Automatic Target Recognition (ATR) plays an important role in military and civil applications, such as social security, environmental monitoring, and national defense [
Since Hintion and Salakhutdinov proposed the Deep Auto-Encoder networks [
For current SAR image database, a hierarchical recognition system (HRS) with combining Deep Belief Network (DBN) and pattern classifier is proposed in this paper. The proposed HRS has both advantages of deep structure and pattern recognition. Based on the great reconstruction ability of DBN, the features can be obtained in each layer. These features can be fed to classifier for high performance recognition.
Meanwhile, in order to obtain sparse feature representation, the Constrained Restricted Boltzmann Machine (CRBM) is defined based on a generalized optimization problem. Unlike the Sparse RBM (SRBM) constrains, the expectation of the hidden units to a certain value, the constraint in CRBM is performed on the probability density of hidden units directly to obtain more sparse solution. Three RBM variants with norm constraint,
From the performance on MSTAR public dataset, the proposed HRS with CRBM can effectively solve the small dataset recognition problem and outperforms current pattern recognition methods in SAR ATR, like PCA + SVM, LDA + SVM, and NMF + SVM [
The contribution of this paper includes two aspects: one is a hierarchical recognition system built for SAR ATR, which can obtain hierarchical features for recognition. The other is the CRBM proposed to obtain more natural sparse feature representation and introduced to HRS for better performance.
The rest of this paper is organized as follows. Section
The purpose of the the proposed Hierarchical Recognition System is to solve small data classification problems by combining the deep structure and the pattern classifiers. The framework of HRS is shown in Figure
The framework of proposd hierarchical recognition system based on deep structure.
Suppose the deep structure in HRS has
The deep structure of Deep Belief Networks (DBN) is mainly discussed in this paper. The DBN is stacked by Restricted Boltzmann Machines (RBMs). In Figure
Actually, the deep structure is not only from DBN but can be from Stacked Auto-Encoder [
Just like the feed forward perception in neural network, the features in Layer
The hierarchical features of the training and test samples obtained by DBN can be treated as the pattern features and fed to the pattern classifier for recognition work directly.
Due to the textural characters of SAR images, sparse representation is beneficial for SAR ATR [
The DBN is stacked by multiple RBMs. The RBM is a particular type of Markov random field that has a two-layer architecture [
RBM model.
An RBM has one visual layer and one hidden layer. The visible units
The update of parameters
It is believed that solving the reconstruction minimal error optimization problem by sparse constraint can obtain better performance in feature representation. For sparse representation, the SRBM constrains the activation of the hidden units at a fixed level
The updating of the log-likelihood term can be computed by CD learning. The right-hand side of (
The SRBM constrains the expectation of the hidden units values on RBM for sparse representation but does not constrain the probability density function of hidden units directly. In this paper, Constrained RBM (CRBM) is proposed by extending (
Different from SRBM, which constrains the average activation probability expectation of the hidden units values, the constraint to RBM in (
In (
Introducing CRBM to HRS will build the Constrained HRS (CHRS). The CHRS with
To verify the performance of the proposed HRS, in this section, the HRS are compared with DBN and some pattern recognition methods, like PCA + SVM, LDA + SVM, and NMF + SVM. The experiments are performed on a “small” dataset.
The SAR images data are taken from MSTAR public database [
Training and test data from MSTAR.
Class | Training | Test | ||
---|---|---|---|---|
Type | Size | Type | Size | |
BMP2 | sn-9563 | sn-9563 | 195 | |
sn-9566 | sn-9566 | 196 | ||
sn-c21 | 233 | sn-c21 | 196 | |
|
||||
BTR70 | sn-c71 | 233 | sn-c71 | 196 |
|
||||
T72 | sn-132 | 232 | sn-132 | 196 |
sn-812 | sn-812 | 195 | ||
sn-s7 | sn-s7 | 191 | ||
|
||||
Total |
|
|
The sample number in MSTAR is in hundreds level. Compared to the standard databases for Deep Learning algorithms, MNIST, CIFAR, and ImageNet databases, which have tens of thousand samples [
To build the proposed HRS, the DBN and HRS are stacked by two RBMs or CRBMs layers. Thus, the DBN has five variants: DBN(RBM), DBN(SRBM), DBN(
The SVM is chosen for pattern classifier. The HRS built for experiments in this section is shown is Figure
The structure of HRS with two RBMs or CRBMs layers used in the experiments.
Both of the two layers in DBN and HRS have 300 hidden units. The input sample has 4096 (
The experiments mainly include two aspects. One is to show the performance of features in each DBN layer the other one is to compare the performance of different recognition methods.
Table
The performance of HRS and DBN on MSTAR with respect to iteration.
Iteration | FEA_ |
FEA_ |
DBN + feedforward |
---|---|---|---|
50 | 92.97% | 92.82% | 91.50% |
100 | 94.21% | 92.53% | 92.31% |
150 | 94.87% | 93.11% | 92.53% |
200 | 94.43% | 93.41% | 92.89% |
300 | 94.36% | 93.85% | 93.41% |
400 | 94.87% | 94.29% | 94.07% |
500 | 94.58% | 94.07% | 93.99% |
Form Table
Besides, the performance of feature
Please note that, in Table
The comparison between pattern recognition methods and HRS is shown in Table
The recognition rates obtained by different methods.
Methods | BMP2 | BTR70 | T72 | Average |
---|---|---|---|---|
PCA + SVM | 88.42% | 94.39% | 92.96% | 91.21% |
LDA + SVM | 79.56% | 96.94% | 85.91% | 84.76% |
NMF + SVM | 90.12% | 99.49% | 93.81% | 93.04% |
DBN (RBM) | 86.88% | 99.49% | 96.74% | 92.89% |
DBN (SRBM) | 86.88% | 99.49% | 97.08% | 93.04% |
DBN ( |
87.05% | 99.49% | 97.25% | 93.19% |
DBN ( |
87.05% | 99.49% | 97.08% | 93.11% |
DBN ( |
89.78% | 99.49% | 97.60% | 94.51% |
HRS (RBM) | 89.61% | 99.49% | 97.60% | 94.43% |
HRS (SRBM) | 89.95% | 99.49% | 98.11% | 94.73% |
HRS ( |
90.12% | 100% | 98.45% | 95.09% |
HRS ( |
90.12% | 99.49% | 98.28% | 94.95% |
HRS ( |
90.46% | 100% | 98.80% | 95.31% |
From Table
Comparing the five DBN variants, it can be seen that the DBN with sparse constraint can obtain better performance than DBN. The DBN(
Comparing the HRS variants to DBN variants, it can be seen that the proposed HRS has better performance than DBN. Thus, the effectiveness of the proposed HRS can be verified.
Overall, the results in Tables
The hierarchical recognition system (HRS) based on Deep Belief Network (DBN) is proposed to solve SAR Automatic Target Recognition (SAR ATR) problem. In HRS, the deep structure of DBN is combined with pattern classifier to solve small data classification problems. The hierarchical features are obtained by the multiple RBMs which is stacked in DBN, and then are fed to pattern classifier directly. To obtain more natural sparse feature representation, the Constrained RBM (CRBM) is proposed with solving a generalized optimization problem. Three RBM variants,
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China under Project 61271287 and China Scholarship Council (no. 201306070061).