1-范数筛分快速匹配超光谱图像算法

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"Rapid matching algorithm for hyperspectral image based on norm sifting" 这篇论文提出了一种快速的高光谱图像光谱匹配算法，通过减少比较次数来节省处理时间。在高光谱图像处理中，光谱匹配是一项关键任务，它涉及到寻找与特定光谱最相似的图像像素或区域，通常用于地物识别、遥感分析等应用。首先，论文采用1-范数（L1范数）作为光谱的长度度量标准。1-范数是向量各元素绝对值之和，相比于其他范数（如2-范数或无穷范数），1-范数在处理稀疏数据时更有效，且对于异常值不那么敏感。通过这个标准，可以构建一个基于1-范数的数据库，存储所有参考光谱的1-范数值。接下来，从完整的参考库中构建一个子空间。这个子空间由那些具有最接近1-范数值的参考光谱组成。选择这种方法的原因在于，它允许我们在一个相对较小的、但包含最相关信息的子集上进行匹配操作，而不是在整个庞大的参考库中进行，从而大大减少了计算复杂性。最后，匹配操作在该子空间内执行，以得出匹配结果。通过这种方式，可以有效地减少处理时间和提高匹配的效率。论文中的模拟实验使用了ASTER（Advanced Spaceborne Thermal Emission and Reflection Radiometer）光谱库进行地质映射，结果显示，提出的算法显著降低了处理时间并提升了匹配的准确性。这篇论文的贡献在于提供了一个实用的优化策略，尤其是在处理大规模高光谱数据时，能够有效提高匹配速度而不牺牲太多精度。这对于实时或近实时的高光谱数据分析场景尤其重要，例如环境监测、灾害响应或军事侦察等。同时，1-范数的选择也为处理噪声和不完整数据提供了额外的鲁棒性。

COL 10(1), 013001(2012) CHINESE OPTICS LETTERS January 10, 2012

Rapid matching algorithm for hyperspectral image based on

norm sifting

Hao Li (李李李皞皞皞)

1,2

, Yong Ma (马马马泳泳泳)

1,2∗

, Kun Liang (梁梁梁琨琨琨)

1,2

, and Yin Yu (余余余寅寅寅)

1,2

Department of Electronics and Information Engineering, Huazhong University of

Science and Technology, Wuhan 430074, China

Wuhan National Laboratory for Optoelectronics, Wuhan 430074, China

∗

Corresp onding author: mayong@hust.edu.cn

Received February 28, 2011; accepted June 14, 2011; posted online August 24, 2011

We propose a rapid spectral matching method by lowering number of comparisons, pro cessing time can be

saved. Firstly, 1-norm is chosen as length measure of spectrum, and with this criterion, a 1-norm database

is built. Secondly, a subspace is constructed from the whole reference library by retaining the references

with the most similar 1-norm values. Finally, matching operations are performed in the subspace to obtain

the match result. Simulations of geological mapping with ASTER spectral library show that the proposed

metho d can significantly reduce processing time and enhance accuracy compared with traditional and

dimension reduction methods.

OCIS codes: 300.6340, 280.4991.

doi: 10.3788/COL201210.013001.

Hyperspectral images provide both spatial and spectral

information with fine resolution. Analysis of hyperspec-

tral data has been applied to environment monitoring, ge-

ological mapping, target recognition, etc.

[1−3]

. Lately the

study of hyperspectral image processing has been mainly

focused on anomaly detection, mixture analysis and clas-

sification methods according to specific applications

[4]

On the other hand, as a pre-processing step of these

methods, techniques of band selection, feature extrac-

tion, and dimension reduction are also topics of inter-

est. They deal with the problem of high dimensionality

of hyperspectral data

[5]

, which is of great importance in

applications like military target detection where the pro-

cessing speed really matters

[6]

. Spectral matching pro-

grams also benefit from these methods, compared to tra-

ditional spectral matching measures like Euclidean dis-

tance (ED) and spectral angle measure (SAM)

[7,8]

, after

dimensional reduction, redundant spectral information is

removed, therefore the calculation complexity is reduced.

In recent years, numerous dimension reduction meth-

ods have been proposed

[9−12]

to avoid redundancy be-

tween bands. For spectral matching tasks, a feasible di-

mension reduction method is band selection

[13−17]

. Guo

et al. proposed a band selection method based on mu-

tual information (MI)

[16]

. The method estimates MI val-

ues using priori knowledge of a reference dataset, and by

eliminating bands with low MI values, which result in the

reduction of the computational cost of spectral matching.

Another method, proposed by Li et al. is called adaptive

band selection algorithm (ABS)

[17]

, which retains bands

with the largest possible amount of information and the

least correlation among them. Similarly, the method is

capable of reducing the computational cost of matching

algorithms.

These methods are designed to reduce the dimensions

of every single spectrum by eliminating redundant bands,

in this way the calculation time required for each compar-

ison between spectra will be reduced. However, a great

number of comparisons are still needed during spectral

matching procedure, which is especially true when the

spectral library contains a large quantity of reference

spectra. Therefore the total processing time for spec-

tral matching is still problematic for certain applications.

Band selection methods overlooked this factor, so it is

necessary to develop a method to reduce matching time

by avoiding unwanted comparisons.

In this letter, a new sp ectral matching algorithm based

on norm information of spectrum is prop osed, by lower-

ing the numb er of comparisons, processing time can be

saved. Reference spectra in spectral library are viewed

as n-dimensional vectors, which are sparsely distributed

in an n-dimensional space. The 1-norm values of these

vectors are calculated and used as an index for sifting.

When a pixel is analyzed, reference spectra with similar

1-norm values are retained and subsequently compared

with the pixel. In this method, spectral matching is pro-

cessed inside a significantly smaller subspace rather than

in the entire n-dimensional space. As fewer comparisons

are needed, time consumption is considerably decreased.

In geographical mapping applications, sp ectral match-

ing algorithm performs a pixel-by-pixel analysis for an

image containing N pixels with n bands. Each pixel is

compared with M reference spectrums in the library to

determine the most similar material. The time needed

for these operations can be expressed as follows:

= M × (T

+ T

) × N, (1)

where T

refers to the reading and writing time of a ref-

erence spectrum record and T

stands for time spent on

comparison operations.

A sp ectrum with n bands can be viewed as a vector

= {x

, x

, · · · , x

} in n-dimensional space. The dis-

tance between target spectrum x

and a reference spec-

trum y

can be calculated using spectral similarity mea-

sures. Two of the most popular similarity measures are

ED and SAM

[7]

. They are expressed as

1671-7694/2012/013001(4) 013001-1

° 2012 Chinese Optics Letters

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