三维SAR聚焦：压缩感测在Angel Stadium的应用

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"通过压缩感测的三维SAR聚焦：Angel Stadium案例研究" 这篇研究论文深入探讨了一种基于压缩感测（Compressive Sensing, CS）的三维合成孔径雷达（Synthetic Aperture Radar, SAR）聚焦方法，并以Angel Stadium为例进行了实际应用分析。在传统的SAR成像中，为了获得高分辨率的图像，需要大量的数据采样，这通常会增加数据处理的复杂性和存储需求。而压缩感测则提供了一种新的途径，它能够在减少数据采集量的同时，保持良好的成像质量。一、压缩感测与SAR成像压缩感测是一种信号处理技术，其核心思想是利用信号的稀疏性，通过较少的采样点获取信号的完整信息。在SAR成像领域，这一理论可以应用于三维SAR tomography，即在正常-斜距方向（normal-slant-range direction）形成一个虚拟的长焦距，以实现对目标的高分辨率成像，尤其是在垂直方向上的分辨能力。二、理论基础论文首先简要回顾了压缩感测在SAR成像中的应用，阐述了如何将CS理论应用于SAR tomography。最新的CS改进理论使得在降低测量数量的同时，仍能保持良好的重建效果。这种方法能够有效地解决传统SAR成像中数据采集和处理的挑战，尤其是在处理大量数据时，显著降低了计算负担。三、Angel Stadium案例研究论文以Angel Stadium为例，使用Envisat-ASAR数据进行了三维重建实验。通过应用提出的聚焦方法，研究人员不仅进行了理论分析，还对真实数据进行了处理，结果表明，这种基于压缩感测的SAR tomographic聚焦方法在实际应用中表现出色，证实了其在三维SAR成像中的可行性。四、关键词该研究涉及的主要关键词包括：压缩感测(CS)，Envisat-ASAR，合成孔径雷达(SAR)，以及 tomography。这些关键词反映了论文的核心技术和所使用的遥感设备，同时也强调了该研究在SAR成像技术上的创新点。这篇研究论文展示了压缩感测在三维SAR聚焦中的潜力，通过实证分析证明了该方法在减少数据采样需求的同时，依然能够获得高质量的三维SAR图像。这对于未来的SAR成像技术发展，特别是在地球观测、环境监测等领域，具有重要的理论和实践意义。

IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 9, NO. 4, JULY 2012 759

Three-Dimensional SAR Focusing via Compressive

Sensing: The Case Study of Angel Stadium

Sun Xilong, Yu Anxi, Dong Zhen, and Liang Diannong

Abstract—Recently, a synthetic aperture radar (SAR) tomo-

grahic focusing method based on compressive sensing was pro-

posed. This focusing method can reduce the required number of

measurements and achieve satisfying elevation resolving ability.

First, we brieﬂy review this novel focusing method and prove the

applicability of compressed sensing (CS) for SAR tomography the-

oretically using the latest improvement of CS. Then, we apply this

focusing method to the 3-D reconstruction of Angel Stadium with

Envisat-ASAR data. Both the theoretical analysis and satisfying

results of real data processing conﬁrmed the applicability of this

SAR tomograhic focusing method.

Index Terms—Compressive sensing (CS), Envisat-ASAR, syn-

thetic aperture radar (SAR), tomography.

I. INTRODUCTION

YNTHETIC aperture radar (SAR) tomography forms a

synthetic aperture along the normal-slant-range (nsr) direc-

tion to achieve resolving ability of multiple scatterers within

one range-azimuth resolution cell [1], [2]. SAR tomography

enables SAR to have the ability of 3-D imaging, so it has at-

tracted an explosion of interest in the last few years. At present,

the synthetic aperture along nsr direction of SAR tomography

is usually achieved by repeat-pass missions of single-antenna

SAR systems. In this data acquisition mode, particularly for

spaceborne SAR, the passes are unevenly spaced, and available

passes are much lower than that needed for a large synthetic

aperture. Hence, the urgent problem of SAR tomography is how

to achieve satisfying elevation resolution with a small number

of nonuniform passes.

Recently, a SAR tomograhic focusing method based on

compressive sensing, in which the inverse problem of SAR

tomography is solved by 

-norm regularization, was proposed

in [3]–[5]. This SAR tomographic focusing method can reduce

the required number of measurements and achieve satisfying

elevation resolving ability with a given aperture in nsr direction.

In [3] and [4], the required number of measurements was

discussed, and experimental results of ERS1/2 data were pre-

sented. In [5], Super-resolution properties and point localization

Manuscript received May 11, 2011; revised October 19, 2011; accepted

December 2, 2011. Date of publication February 23, 2012; date of current

version May 7, 2012. This work is supported by the National Natural Science

Foundation of China (61002031, 61101187) and NUDT Research Foundation

(JC10-04-03).

The authors are with School of Electronic Science and Engineer-

ing, National University of Defense Technology, Changsha 410073, China

(e-mail: longlongsun@sohu.com; yu_anxi@sina.com; dongzhen@vip.sina.

com; 396576571@qq.com).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/LGRS.2011.2181321

Fig. 1. Multipass acquisition geometry of SAR tomography. For the sake of

simplicity, all the acquisitions are aligned along normal-slant-range direction.

accuracies of this focusing method were demonstrated using

simulations and real TerraSAR-X data.

In SAR tomography, the measurements are random sam-

ples of continuous frequency spectrum of the unknown sig-

nal, instead of random samples of discrete Fourier transform

(DFT). As a consequence, the sensing matrix is not obtained

by randomly sampling rows of an orthonormal matrix. The

theory of CS in [6]–[11] cannot provide a framework for this

measurement strategy perfectly. Recently, Candes introduced a

simple and very general theory of compressive sensing in [12]

that can provide a framework for the measurement strategy in

SAR tomography. In this letter, we will prove the applicability

of compressed sensing (CS) for SAR tomography theoretically

using the theory in [12]. Then, we will apply the CS-based

focusing method to real data to validate this method. The

Envisat -ASAR data over Angel Stadium between October 29th

2003 and November 7th 2007 are used.

II. F

ORMULATION OF SAR TOMOGRAPHY

To achieve resolving ability of multiple scatterers within one

azimuth-range resolution cell, a synthetic aperture along the nsr

direction is needed to form by repeat-pass missions of single-

antenna SAR system. Fig. 1 gives the multipass acquisition

geometry, for the sake of simplicity, all the acquisitions are

aligned along nsr direction. Let us refer to the condition that

M passes are acquired over the target with different baselines.

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