基于贝叶斯压缩感知的四维SAR稀疏成像方法

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本文主要探讨了"贝叶斯压缩感知在四维合成孔径雷达（4-DSAR）稀疏成像中的应用"。随着技术的发展，传统的SAR系统已能实现全天候的二维图像获取，而SAR tomography进一步提升了分辨率，扩展到三维成像。然而，针对4-DSAR所特有的接收到的数据稀疏且非均匀特性，研究人员提出了一个新的方法，旨在利用贝叶斯压缩感知理论进行更为高效和精确的四维成像。首先，作者分析了4-DSAR系统的信号特征，认识到其数据在高度和速度维度上具有天然的稀疏性，这与压缩感知理论中的关键假设相符，即许多实际信号在某些变换下是稀疏表示的。在这个背景下，传统的脉冲压缩技术被用来首先获取水平-斜距（azimuth-slant range）图像，这是4-DSAR成像的基础步骤。接着，文章的核心部分引入了贝叶斯压缩感知算法。不同于经典的压缩感知，贝叶斯方法考虑了先验信息和不确定性，允许对观测数据进行更精细的建模。通过这种概率模型，即使在数据量有限的情况下，也能有效估计出高度-速度（height-velocity）图像，从而实现四维空间的高精度重建。通过模拟实验，该方法的有效性得到了验证。实验结果显示，与传统方法相比，基于贝叶斯压缩感知的4-DSAR成像方法能够在保持较低采样率的同时，显著提高图像质量和细节恢复能力，特别是在处理非均匀分布的信号时，优势更为明显。本研究不仅提升了4-DSAR的成像性能，而且为稀疏信号处理领域提供了新的思路，尤其是在高分辨率、多维度遥感应用中具有重要的实践价值。关键词包括合成孔径雷达、四维成像、稀疏成像以及贝叶斯压缩感知，这些都是理解本文核心内容的关键术语。

Four-Dimensional SAR Sparse Imaging Using

Bayesian Compressive Sensing

Xiaozhen Ren, Lihong Qiao, and Lianjie Tian

College of Information Science and Engineering,

Henan University of Technology

Zhengzhou, China

Abstract—As the received data obtained by 4-D SAR is sparse

and non-uniform, a new 4-D SAR imaging method based on

Bayesian compressive sensing is proposed in this paper. After the

analysis of the signal characteristics of 4-D SAR system, the 4-D

imaging process can be divided into two steps. The azimuth-slant

range image is acquired by traditional pulse compression first,

and then the height-velocity image is reconstructed based on

Bayesian compressive sensing. Simulation results confirm the

effectiveness of the proposed method.

Index Terms—synthetic aperture radar, four-dimensional,

sparse imaging, Bayesian compressive sensing.

I. INTRODUCTION

Traditional synthetic aperture radar (SAR) systems can

reconstruct two-dimensional (2-D) images of the interested

area with all-weather capability, and SAR tomography extends

the resolution capability of 2-D SAR into the height direction

for 3-D imaging. 4-D SAR imaging, also referred to as

differential SAR tomography, is a natural extension of SAR

tomography [1-3]. It can distinguish the heights and velocities

of different scatterers within the same azimuth-range resolution

cell. Therefore, 4-D imaging technique has resolving

capabilities in the azimuth-range-height-velocity 4-D space.

Unfortunately, for the current 4-D SAR system, the received

data is sparse and non-uniform in the baseline-time plane.

Hence, the imaging results obtained by traditional methods are

limited by high sidelobes.

To overcome the imaging difficulties caused by the spare

aperture data, singular value decomposition (SVD) and

inverse problem based methods were all proposed to achieve

sidelobe reduction [4, 5]. An additional problem is that these

methods should handle an ill-conditioning inverse problem.

Subsequently, also compressive sensing (CS) based method

was considered to focus the height-velocity image [3]. CS is a

model-based framework for data acquisition and signal

recovery based on the premise that a signal having a sparse

representation in one basis can be reconstructed from a small

number of measurements collected in a second basis that is

incoherent with the first [6, 7]. However, the image quality is

unsatisfactory under low SNR level.

In recent years, there has been increased concern over

Bayesian compressive sensing (BCS) [8, 9]. BCS methods can

provide certain improvements when compared with CS

methods in low noise level. Therefore, from the BCS

perspective, we propose a novel algorithm for 4-D SAR

imaging in this paper.

The rest of the paper is organized as follows. Section 2

presents the basis theory of BCS. In Section 3, a new 4-D SAR

imaging scheme based on BCS is described in detail. The

performance of the method is investigated by simulated data in

Section 4. Finally, Section 5 gives a brief conclusion.

II. B

AYESIAN COMPRESSIVE SENSING

Consider a discrete signal

x with a length of L, which has

sparse representation in an orthogonal basis

, and then the

signal

x can be represented as

Ψσ

(1)

where

denotes the projection coefficient vector. If

has

only J nonzero or significant entries, the signal

x can be

considered as J-sparse in orthogonal basis

From the CS framework, the signal

x can be reconstructed

from K (

(log( ))

OJ LJ=⋅ ) measurements

only if the

measurements were obtained in a sensing basis

, which is

mutually incoherent to the basis

, where the mutual

coherency is defined as [6, 7]:

max ,

kj L

μφψ

≤≤

(, )=

ΦΨ

(2)

Therefore, the measurement vector can be written as

+y= x= n

ΦΦΨσ

(3)

Equation (3) could be cast as the classical problem of signal

recovery and denoising in estimation theory. Based on the

theory of Bayesian compressive sensing, the maximum a

posteriori (MAP) estimator can be used to estimate

, which

is expressed as

()

arg max arg max | ,

ppp

σσ

⎡⎤

== ⋅

⎣⎦

σσ σσ

(4)

As for high frequency radars, the targets can be modeled as

sparse based on the hypothesis of multi-center of scattering,

then the back scattering field of the target have stronger

sparsity; that is to say, most energy is contributed by seldom

scattering centers [10]. Therefore, the 4-D SAR imaging can be

transformed into the problem of sparse signal representation,

and BCS-based method can be used for image reconstruction.

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