ICA方法提升SAR图像去斑：增强与分离策略

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本文主要探讨了一种利用独立成分分析（Independent Component Analysis, ICA）基础图像进行合成孔径雷达（Synthetic Aperture Radar, SAR）图像去斑（speckle reduction）的方法。在SAR图像处理领域，散斑噪声（speckle noise）是由于多路径效应导致的一种常见问题，严重影响了图像的细节和可解读性。该研究方法旨在通过ICA技术来改善这一状况。首先，研究人员采用ICA算法对原始SAR图像进行分解，获取一组基础图像（basis images）和对应的代码矩阵（code matrix）。ICA是一种无监督学习方法，能够分离出数据中的非高斯、独立成分，这对于处理复杂的SAR信号特别有用，因为它可以分离出有用的信号特征与噪声。接着，作者提出了一种新的成本准则，即点wise的Holder指数（Pointwise Holder Exponent），用于评估每个基础图像的噪声程度。Holder指数是一种描述函数平滑性的度量，它可以反映图像局部变化的特性。通过计算每个基础图像的Holder指数，研究人员能够识别出那些更接近于理想噪声分布的"干净"基础图像。在得到优化的基础图像后，作者设计了一个分离规则，将这些干净的基础图像与原始图像中的基础进行区分。这种分离策略有助于增强关键步骤的有效性，从而减少散斑噪声的影响。最后，通过在干净的基础图像和原始代码矩阵上进行重构，得到了最终的去斑SAR图像。与传统去斑技术相比，这种方法显示出更好的视觉感知和图像质量，因为ICA能够更精确地捕捉信号的结构信息并有效抑制噪声。这项工作结合了ICA的降噪优势和数学上的特性分析，为SAR图像的去斑提供了一种新颖且有效的解决方案，对于提高遥感图像的解析能力具有重要意义。OCIS分类代码：100.0100（图像处理基础）、030.6140（遥感图像处理）、280.6730（合成孔径雷达系统）以及350.4600（信号处理应用）涵盖了本文的核心研究领域。

September 10, 2007 / Vol. 5, No. 9 / CHINESE OPTICS LETTERS 509

Speckle reduction of SAR images using ICA basis

enhancement and separation

Yutong Li (



) and Yue Zhou (



)

Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, Shanghai 200240

Received April 6, 2007

An approach for synthetic aperture radar (SAR) image de-noising based on independent component anal-

ysis (ICA) basis images is proposed. Firstly, the basis images and the code matrix of the original image

are obtained using ICA algorithm. Then, pointwise H¨older exponent of each basis is computed as a cost

criterion for basis enhancement, and then the enhanced basis images are classified into two sets according

to a separation rule which separates the clean basis from the original basis. After these key procedures

for speckle reduction, the clean image is finally obtained by reconstruction on the clean basis and original

code matrix. The reconstructed image shows better visual perception and image quality compared with

those obtained by other traditional techniques.

OCIS codes: 100.0100, 030.6140, 280.6730, 350.4600.

Synthetic aperture radar (SAR) sensors can produce

range imagery of high spatial resolution under different

conditions. However, the images suffer from the effects

of speckle noise. Thus, speckle reduction is a key step

for desirable image quality. For this application, Lee de-

veloped a linear approximation filter based on the min-

imum mean-square error (MMSE) criterion in 1980

[1]

and Kuan presented a generalized filter of Lee’s in

1985

[2]

. Wavelet thresholding shrinkage was proposed in

1995

[3]

. Taking advantage of the excellent performance

of independent component analysis (ICA), a method

namely sparse code shrinkage was proposed as a novel

improvement

[4]

. However, conventional algorithms lack

consideration on the basis information obtained by in-

dependent component analysis (ICA)

[5]

, which usually

contains substantial knowledge for our denoising work.

Based on extensive study on these meaningful basis, we

propose a novel theory for SAR image dispeckling in this

paper. The proposed method contains two key proce-

dures, basis enhancement and basis separation. As to the

former, we extend the signal enhancement algorithm by

Vehel

[6]

for image application and use pointwise H¨older

exponent as a criterion for basis enhancement; as to the

latter, based on the proposed separation theory and sep-

aration rule, we further classify the enhanced basis into

two types respectively called ‘clean’ basis and ‘noise’ ba-

sis, which belong to corresponding subspaces, ‘clean’ and

‘noise’. After these procedures, the clean image is ob-

tained by reconstruction on the clean basis.

ICA is a statistical method for transforming an ob-

served multi-dimensional random vector into components

that are mutually independent. Denoted by X the ob-

served matrix: X = {x

, ··· ,x

}

,byS the in-

dependent components matrix (or sparse code matrix):

S = {s

, ··· ,s

}

,andbyA(m × n, m > n)the

mixed matrix, the linear representation can be given by

X = AS or S = WX, (1)

where x

(i =1, ··· ,m) is the observed signal and s

(i =1, ··· ,n) is the independent component, W namely

demixed matrix or transformation matrix is the pseudo

inverse of A,thatisW = A

. In the following content,

we replace x

, s

with x, s for short.

The independent components in ICA are obtained by

maximizing non-Gaussianity measure, which is equiva-

lent to searching for sparse representation. Thus, ICA

gives sparse codes for natural images. According to

sparse coding theory

[4]

, the localized and compact dis-

tribution of energy in images suggests that they have a

“sparse structure”, which means any image can be repre-

sented by a relatively small number of descriptors out of

a much larger set to choose from. Thus, an image I(x, y)

can be modelled as a linear superposition of basis φ

which can be defined as

I(x, y)=[



k,b

],k=1, ··· ,n, (2)

where s

k,b

is the element of code matrix S at row k,col-

umn b.Andφ

is the kth column vector of mixed matrix

A =[φ

, ··· ,φ

If we use symbol ‘↔’ to define the mapping associa-

tion between a basis and the corresponding independent

component, we obtain s

↔ φ

, k =1, ··· ,n.

Measuring the local smoothness of functions is proved

to be an important task for many applications in mathe-

matical analysis and in signal and image processing. Such

a characterization is vital in multi-fractal analysis, and

is an instrumental tool for image segmentation and de-

noising. H¨older exponent is considered as a powerful pa-

rameter for studying the structure of singular signals

[7]

Let α ∈ (0, 1), and x

∈ K ⊂ R. A function f : K → R

is in C

(orhasapointwiseH¨older exponent α at x

if for all in a neighborhood x of x

|f(x) − f(x

)|≤c |x − x

, (3)

where c is a constant independent of x

and α.The

H¨older exponent α is computed as

(x) = lim inf

h→0

log |f (x + h) − f(x)|

log |h|

. (4)

Clearly, a function that is differentiable at x = x

has

aH¨older exponent α ≥ 1. Geometrically, this means that

the magnitude of oscillations of the function near x

de-

creases faster than the distance to x. In general, if this

1671-7694/2007/090509-04

 2007 Chinese Optics Letters

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