Progress In Electromagnetics Research Symposium Proceedings, Guangzhou, China, Aug. 25–28, 2014 1027
Microwave Radiation Interferometry High Resolution
Reconstruction Based on Mixed Orthogonal Basis
Chao Song, Lu Zhu, Yuanyuan Liu, and Suhua Chen
School of Information Engineering
East China Jiaotong University, Nanchang 330013, China
Abstract— Microwave radiometry is the primary means of soil moisture remote sensing and
capable of observation soil moisture all-time, all-weather. But the imaging method of traditional
microwave radiometry has complex structure and low resolution, which limited largely the appli-
cation in regional soil moisture remote sensing. In this paper, we propose a new inversion method
for microwave radiation interferometry imaging based on compressed sensing (CS), by mining the
sparse and compressible information of the microwave radiation image. The proposed method
can break through the limit of the inherent spatial resolution of the imaging system which based
on the Nyquist sampling, achieving the spatial resolution image closely obtained by the expensive
large aperture imaging system, and reducing the complexity and the cost of the hardware of the
imaging system configuration. Due to the complexity of microwave radiation image scene, it is
difficult to sparsely represent the microwave radiation image by single orthogonal basis, so we
make use of the sparse representation in mixed orthogonal basis and the constraint conditions
of total variation regularization of microwave radiation image, and establish the optimal recon-
struction model of microwave radiation image. We solve the optimal solution of reconstruction
model by adopting the alternating direction method (ADM), achieve high resolution microwave
radiation image reconstruction from low-dimensional measurements to high -dimensional data,
and solve the contradiction between the high resolution and the complexity of the system, and
establish evaluation methods of spatial resolution. The simulation results show that, compared
with orthogonal the matching pursuit (OMP) algorithm, the proposed algorithm can achieve
higher spatial resolution.
1. INTRODUCTION
Interferometric synthetic aperture microwave radiometry (ISAMR) integrates small aperture an-
tenna array into large observation aperture, without mechanical scanning, can overcome the short-
comings of real aperture microwave radiometer. However, for L-Band space borne ISARM, in order
to achieve a spatial resolution of 50 km, it still needs 9 meters in diameter antenna array. And with
soil moisture sensing area and the fine structure in the direction of development, need increase
the diameter of antenna array to satisfy the high spatial resolution requirement, the resolution of
radiometer data can be enhanced by using either image processing techniques or special recon-
struction algorithms. ISAMR has evolved into a large and complex system that need hundreds
of millions data to imaging. In this regard, interferometry and conventional microwave radiation
imaging method based on spatial Nyquist is difficult to achieve.
Compressed sensing (CS) theory [1] brought a huge breakthrough in the field of information
processing in recent years,and it has changed the way people access information. The CS model is
shown in Figure 1.
Compressible
signal
STEP 1
Sparse transform
x=
Ψ
T
u
STEP 2
Observations obtained
M-dimensional vector:
b=
Φx
STEP 3
Reconstruct signal
Min
||Ψ
T
u||
0
S.t A
cs
u=b
Figure 1: Compressed sensing theoretical framework.
For encoders, recent results indicate that stable reconstructionfor both K-sparse and compress-
ible signals canbe ensured by restricted isometry property (RIP). However, it is extremely difficult
to verify the RIP prop ertyin practice. Fortunately, Candes et al. show that RIP holds with high
probability when the measurement matrix are random. Being under determined, the equation
b = ΦΨ
T
u usually has infinitely many solutions. If we know in advance that b is acquired from a
highly sparse signal, a reasonable approach would be adopted to seek the sparsest one among all
solutions, i.e.,