CN103886639B - A kind of construction method of Pixel Unmixing Models based on anti-noise - Google Patents
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Abstract
Description
【技术领域】【Technical field】
本发明涉及混合像元分解模型的技术领域，特别是基于抗噪的混合像元分解模型的构建方法的技术领域。The invention relates to the technical field of a mixed pixel decomposition model, in particular to the technical field of a construction method of a mixed pixel decomposition model based on anti-noise.
【背景技术】【Background technique】
高光谱图像的产生过程是一个复杂的物理作用过程，物理作用过程发生在光源、材料表面及大气干涉等之间。由此复杂的图像产生过程中，产生了大量的噪声，这些噪声可能包括加性噪声及乘性噪声，且由于包括不止一种噪声，所以还可能产生混合噪声。因此高光谱数据的产生受到多种因素影响.且噪声类型较为复杂，因而在高光谱数据分析过程中，对噪声特点进行分析显得十分重要。研究表明在解释一些现象的过程中依赖于乘性噪声及加性噪声之间的相互作用，如在解释如下现象时：随机共振、在相变及运输超导电节点处等等。有大部分高光谱图像分析算法因为对噪声的良好估计而最终获得较为理想的图像处理结果，如：高光谱图像压缩算法、高光谱图像分析算法等。在实际应用中，我们常常对表面反射率的变化进行估计，譬如光照变化引起的乘性作用及后向散射引起的加性作用，而对于这两种作用均可以看作为噪声。为了很好的评估噪声，必须构建合适的噪声模型，而高光谱数据的噪声模型因高光数据采集过程所使用的高光谱成像传感器的不同而不同。高光谱成像传感器常用拂扫式及推扫式传感器，这两种传感器的差异性决定了噪声特点的差异性，因而需要针对不同的传感器构建不同的噪声模型进行噪声评估。在混合像元分解研究中，常用的实际数据由美国国家航空航天局的喷气推进实验室肮空可见光/红外成像光谱仪获取，而AVIRIS采用的是推扫式(whiskbroom)传感器，推扫式传感器的原理是，利用旋转的镜子沿垂直于传感器平台的方向扫描一侧到另一侧的场景，推扫式成像仪相对于拂扫式成像仪更重、更大且更加复杂，其移动范围较拂扫式成像仪也更大。由推扫式成像仪因为光电扫描机制、非线性传感器、原始数据的预处理、图像空间及光谱空间的相关性等因素所产生的噪声可能不是高斯型噪声。对于所有的光学图像来讲，其信噪比由光子作用或者快照占主导，其中因为随机的光子与检测器之间的作用本质上是乘性噪声，而特别值得注意的是乘性噪声依赖于传感器温度，因此很难对乘性噪声建模从而去矫正乘性噪声。通常，在混合像元分解过程中，需要对输入的高光谱图像数据进行预处理，常见的预处理即光谱归一化处理，光谱归一化的目的就是矫正被乘性噪声污染的光谱并矫正反射光谱光散射的变化。但是遗憾地是，通过这些与处理算法无法彻底去除乘性噪声。而现在的高光谱图像混合像元分解算法却都在假设乘性噪声不存在的情况下，仅仅考虑加性白噪声的影响，这种忽略乘性噪声影响的混合像元分解算法很显然是不合适的。The hyperspectral image generation process is a complex physical process, which occurs between light sources, material surfaces, and atmospheric interference. In the complex image generation process, a large amount of noise is generated, which may include additive noise and multiplicative noise, and since it includes more than one type of noise, mixed noise may also be generated. Therefore, the generation of hyperspectral data is affected by many factors, and the types of noise are relatively complex. Therefore, it is very important to analyze the characteristics of noise in the process of hyperspectral data analysis. Studies have shown that the interaction between multiplicative noise and additive noise is relied upon in the process of explaining some phenomena, such as in explaining the following phenomena: stochastic resonance, at the node of phase transition and transport superconductivity, etc. Most hyperspectral image analysis algorithms finally obtain ideal image processing results because of good estimation of noise, such as: hyperspectral image compression algorithm, hyperspectral image analysis algorithm, etc. In practical applications, we often estimate changes in surface reflectance, such as the multiplicative effect caused by illumination changes and the additive effect caused by backscattering, and both effects can be regarded as noise. In order to evaluate the noise well, it is necessary to construct a suitable noise model, and the noise model of hyperspectral data varies with the hyperspectral imaging sensor used in the hyperspectral data acquisition process. Hyperspectral imaging sensors are commonly used in brush-broom and push-broom sensors. The difference between these two sensors determines the difference in noise characteristics. Therefore, it is necessary to build different noise models for different sensors for noise evaluation. In the study of mixed pixel decomposition, the commonly used actual data is obtained by the dirty visible light/infrared imaging spectrometer of NASA's Jet Propulsion Laboratory, while AVIRIS uses a push-broom (whiskbroom) sensor. The principle is that using rotating mirrors to scan the scene from one side to the other in a direction perpendicular to the sensor platform, push-broom imagers are heavier, larger, and more complex than brush-broom imagers, and their range of movement is longer than that of brush-broom imagers. The scanning imager is also larger. The noise generated by the push-broom imager due to factors such as photoelectric scanning mechanism, nonlinear sensor, raw data preprocessing, image space and spectral space correlation may not be Gaussian noise. For all optical images, the signal-to-noise ratio is dominated by photon interactions or snapshots, because random photon-detector interactions are inherently multiplicative noise, and it is particularly noteworthy that multiplicative noise depends on Sensor temperature, so it is difficult to model multiplicative noise to correct for multiplicative noise. Usually, in the process of decomposing mixed pixels, it is necessary to preprocess the input hyperspectral image data. The common preprocessing is spectral normalization processing. The purpose of spectral normalization is to correct the spectrum polluted by multiplicative noise and correct Changes in reflectance spectrum light scattering. But unfortunately, the multiplicative noise cannot be completely removed by these AND processing algorithms. However, the current hybrid pixel decomposition algorithms for hyperspectral images only consider the influence of additive white noise under the assumption that multiplicative noise does not exist. suitable.
【发明内容】【Content of invention】
本发明的目的就是解决现有技术中的问题，提出一种基于抗噪的混合像元分解模型的构建方法，能够通过基于抗噪的混合像元分解模型来克服加性噪声、乘性噪声及混合噪声对高光谱图像混合像元分解的影响。The purpose of the present invention is to solve the problems in the prior art, and propose a method for constructing a mixed pixel decomposition model based on anti-noise, which can overcome additive noise, multiplicative noise and The Effect of Mixed Noise on the Decomposition of Mixed Pixels in Hyperspectral Imagery.
为实现上述目的，本发明提出了一种基于抗噪的混合像元分解模型的构建方法，依次包括以下步骤：In order to achieve the above object, the present invention proposes a method for building a mixed pixel decomposition model based on anti-noise, which includes the following steps in turn:
a)在图像处理过程中考虑乘性噪声的影响因素，所述乘性噪声在信号独立性方面满足非高斯分布，且乘性噪声随着图像空间的变化而变化，于是给出抗噪模型：其中是指包括了多种噪声的混合像元矩阵，表示从含有多种噪声的混合像元矩阵X中提取的端元矩阵，代表相应的端元丰度矩阵，表示随机测量误差矩阵，表示乘性噪声，式中M表示光谱波段数，N表示像素个数，K表示端元个数；a) Consider the influence factors of multiplicative noise in the image processing process, the multiplicative noise satisfies the non-Gaussian distribution in terms of signal independence, and the multiplicative noise changes with the change of image space, so the anti-noise model is given: in refers to the mixed pixel matrix including various noises, Represents the endmember matrix extracted from the mixed pixel matrix X containing various noises, represents the corresponding endmember abundance matrix, represents the random measurement error matrix, Represents multiplicative noise, where M represents the number of spectral bands, N represents the number of pixels, and K represents the number of endmembers;
b)采用常用的欧几里德距离及交替最小二乘算法推导我们提出的抗噪模型的解混结果，并由均方差准则MSE定量评估抗噪模型混合像元分解性能：b) Using the commonly used Euclidean distance and alternating least squares algorithm to derive the unmixing results of our anti-noise model, and quantitatively evaluate the mixed pixel decomposition performance of the anti-noise model by the mean square error criterion MSE:
b1)由公式可以得到X≈WHρ，从公式X≈WHρ中可推导H： 表示乘性噪声矩阵ρ的伪逆矩阵，令UW＝(WTW)-1WT为端元矩阵W的伪逆矩阵，那么计算抗噪模型的丰度矩阵的均方差误差为： b1) by the formula X≈WHρ can be obtained, and H can be derived from the formula X≈WHρ: Represents the pseudo-inverse matrix of the multiplicative noise matrix ρ, let U W = (W T W) -1 W T is the pseudo-inverse matrix of the endmember matrix W, then Computational Noise Resistant Model The mean square error of the abundance matrix of is:
b2)若固定丰度矩阵H，求解端元矩阵W，可推导抗噪模型的提取端元的精确性，即首先从公式X≈WHρ推导W，令VH＝(HTH)-1HT为矩阵H的伪逆矩阵，那么则计算抗噪模型的端元矩阵的均方差误差为： b2) If the abundance matrix H is fixed and the endmember matrix W is solved, the accuracy of the extracted endmembers of the anti-noise model can be derived, that is, W is first derived from the formula X≈WHρ, and V H =(H T H) -1 H T is the pseudo-inverse matrix of matrix H, So Then calculate the anti-noise model The mean square error of the endmember matrix of is:
c)基于IS距离将抗噪模型：进行优化处理，并转化为新的优化模型： c) Anti-noise model based on IS distance: Perform optimization processing and convert to a new optimized model:
其中DIS(X||WH)表示IS距离，d(ω||υ)表示尺度代价函数， 分别表示实测的丰度矩阵及实测的端元矩阵，s.t.表示约束条件，wij、hjt分别表示端元矩阵及丰度矩阵中的元素，ζH表示计算的丰度矩阵与实测的丰度矩阵之间的差值，ζW表示计算的端元矩阵与实测的端元矩阵之间的差值。where D IS (X||WH) represents the IS distance, d(ω||υ) represents the scale cost function, Represents the measured abundance matrix and the measured endmember matrix respectively, st represents the constraint condition, w ij , h jt represent the elements in the endmember matrix and the abundance matrix respectively, ζ H represents the calculated abundance matrix and the measured abundance The difference between matrices, ζ W represents the difference between the calculated endmember matrix and the measured endmember matrix.
作为优选，所述步骤a)中的端元丰度矩阵H应满足每列和为一条件，且W矩阵和H矩阵均为非负矩阵；随机测量误差矩阵的产生来源包括加性噪声及混合噪声，所述混合噪声为由加性噪声跟乘性噪声组合成的噪声；所述乘性噪声随着空间上逐个像素的光照变化而变化，乘性噪声遵循伽马分布，并且满足独立同分布，乘性噪声ρ也是一个非负矩阵。As preferably, the endmember abundance matrix H in the step a) should satisfy the condition that each column sum is one, and both the W matrix and the H matrix are non-negative matrices; random measurement error matrix The sources of generation include additive noise and mixed noise, the mixed noise is the noise composed of additive noise and multiplicative noise; the multiplicative noise changes with the spatially pixel-by-pixel illumination change, and the multiplicative noise follows Gamma distribution, and satisfying the independent and identical distribution, the multiplicative noise ρ is also a non-negative matrix.
作为优选，所述IS距离属于布格雷曼距离的一种，IS距离能够很好测量两个光谱之间的距离，IS距离使用最大似然方法重构信号中的成份，IS距离在重构信号时具有良好动感知性；在伽马噪声服从均值为1的独立同分布时，IS距离是序族分离度中的唯一一个具有尺度不变性的距离，对乘性噪声不敏感。Preferably, the IS distance belongs to a kind of Bougreyman distance, and the IS distance can measure the distance between two spectra well. The IS distance uses the maximum likelihood method to reconstruct the components in the signal, and the IS distance is used in the reconstructed signal. It has good dynamic perception; when the gamma noise obeys the independent and identical distribution with a mean of 1, the IS distance is the only scale-invariant distance in the sequence family separation degree, and it is not sensitive to multiplicative noise.
本发明的有益效果：本发明通过构建基于抗噪的混合像元分解模型来克服加性噪声、乘性噪声及混合噪声对高光谱图像混合像元分解的影响，本模型根据IS距离的统计特性，有效地克服乘性噪声的影响，从而避免产生混合噪声，获得较为精确的信号重构，提高混合像元分解结果的精度，并对抗噪模型进行理论推导，证明了基于抗噪模型的混合像元分解的可行性及优越性。Beneficial effects of the present invention: the present invention overcomes the influence of additive noise, multiplicative noise and mixed noise on the decomposition of hyperspectral image mixed pixels by constructing an anti-noise-based mixed pixel decomposition model. This model is based on the statistical characteristics of IS distance , effectively overcome the influence of multiplicative noise, thereby avoiding mixed noise, obtaining more accurate signal reconstruction, improving the accuracy of mixed pixel decomposition results, and theoretically deriving the anti-noise model, proving that the mixed image based on the anti-noise model Feasibility and superiority of meta-decomposition.
【具体实施方式】【detailed description】
本发明一种基于抗噪的混合像元分解模型的构建方法，依次包括以下步骤：A kind of construction method of the mixed pixel decomposition model based on anti-noise of the present invention, comprises the following steps successively:
a)在图像处理过程中考虑乘性噪声的影响因素，所述乘性噪声在信号独立性方面满足非高斯分布，且乘性噪声随着图像空间的变化而变化，于是给出抗噪模型：其中是指包括了多种噪声的混合像元矩阵，表示从含有多种噪声的混合像元矩阵X中提取的端元矩阵，代表相应的端元丰度矩阵，表示随机测量误差矩阵，表示乘性噪声，式中M表示光谱波段数，N表示像素个数，K表示端元个数；a) Consider the influence factors of multiplicative noise in the image processing process, the multiplicative noise satisfies the non-Gaussian distribution in terms of signal independence, and the multiplicative noise changes with the change of image space, so the anti-noise model is given: in refers to the mixed pixel matrix including various noises, Represents the endmember matrix extracted from the mixed pixel matrix X containing various noises, represents the corresponding endmember abundance matrix, represents the random measurement error matrix, Represents multiplicative noise, where M represents the number of spectral bands, N represents the number of pixels, and K represents the number of endmembers;
b)采用常用的欧几里德距离及交替最小二乘算法推导我们提出的抗噪模型的解混结果，并由均方差准则MSE定量评估抗噪模型混合像元分解性能：b) Using the commonly used Euclidean distance and alternating least squares algorithm to derive the unmixing results of our anti-noise model, and quantitatively evaluate the mixed pixel decomposition performance of the anti-noise model by the mean square error criterion MSE:
b1)由公式可以得到X≈WHρ，从公式X≈WHρ中可推导H： 表示乘性噪声矩阵ρ的伪逆矩阵，令UW＝(WTW)-1WT为端元矩阵W的伪逆矩阵，那么计算抗噪模型的丰度矩阵的均方差误差为： b1) by the formula X≈WHρ can be obtained, and H can be derived from the formula X≈WHρ: Represents the pseudo-inverse matrix of the multiplicative noise matrix ρ, let U W = (W T W) -1 W T is the pseudo-inverse matrix of the endmember matrix W, then Computational Noise Resistant Model The mean square error of the abundance matrix of is:
b2)若固定丰度矩阵H，求解端元矩阵W，可推导抗噪模型的提取端元的精确性，即首先从公式X≈WHρ推导W，令VH＝(HTH)-1HT为矩阵H的伪逆矩阵，那么则计算抗噪模型的端元矩阵的均方差误差为： b2) If the abundance matrix H is fixed and the endmember matrix W is solved, the accuracy of the extracted endmembers of the anti-noise model can be derived, that is, W is first derived from the formula X≈WHρ, and V H =(H T H) -1 H T is the pseudo-inverse matrix of matrix H, So Then calculate the anti-noise model The mean square error of the endmember matrix of is:
c)基于IS距离将抗噪模型：进行优化处理，并转化为新的优化模型： c) Anti-noise model based on IS distance: Perform optimization processing and convert to a new optimized model:
其中DIS(X||WH)表示IS距离，d(ω||υ表示尺度代价函数， 分别表示实测的丰度矩阵及实测的端元矩阵，s.t.表示约束条件，wij、hjt分别表示端元矩阵及丰度矩阵中的元素，ζH表示计算的丰度矩阵与实测的丰度矩阵之间的差值，ζW表示计算的端元矩阵与实测的端元矩阵之间的差值。where D IS (X||WH) represents the IS distance, d(ω||υ represents the scale cost function, Represents the measured abundance matrix and the measured endmember matrix respectively, st represents the constraint condition, w ij , h jt represent the elements in the endmember matrix and the abundance matrix respectively, ζ H represents the calculated abundance matrix and the measured abundance The difference between matrices, ζ W represents the difference between the calculated endmember matrix and the measured endmember matrix.
所述步骤a)中的端元丰度矩阵H应满足每列和为一条件，且W矩阵和H矩阵均为非负矩阵；随机测量误差矩阵的产生来源包括加性噪声及混合噪声，所述混合噪声为由加性噪声跟乘性噪声组合成的噪声；所述乘性噪声随着空间上逐个像素的光照变化而变化，乘性噪声遵循伽马分布，并且满足独立同分布，乘性噪声ρ也是一个非负矩阵，所述IS距离属于布格雷曼距离的一种，IS距离能够很好测量两个光谱之间的距离，IS距离使用最大似然方法重构信号中的成份，IS距离在重构信号时具有良好动感知性；在伽马噪声服从均值为1的独立同分布时，IS距离是序族分离度中的唯一一个具有尺度不变性的距离，对乘性噪声不敏感。The endmember abundance matrix H in the step a) should meet the condition that each column sum is a condition, and both the W matrix and the H matrix are non-negative matrices; random measurement error matrix The sources of generation include additive noise and mixed noise, the mixed noise is the noise composed of additive noise and multiplicative noise; the multiplicative noise changes with the spatially pixel-by-pixel illumination change, and the multiplicative noise follows Gamma distribution, and satisfy independent and identical distribution, the multiplicative noise ρ is also a non-negative matrix, the IS distance belongs to a kind of Bugreyman distance, the IS distance can measure the distance between two spectra well, the IS distance uses The maximum likelihood method reconstructs the components in the signal, and the IS distance has good dynamic perception when reconstructing the signal; when the gamma noise obeys the independent and identical distribution with a mean of 1, the IS distance is the only one in the sequence family separation with a scale Invariant distance, insensitive to multiplicative noise.
本发明通过构建基于抗噪的混合像元分解模型来克服加性噪声、乘性噪声及混合噪声对高光谱图像混合像元分解的影响，本模型根据IS距离的统计特性，有效地克服乘性噪声的影响，从而避免产生混合噪声，获得较为精确的信号重构，提高混合像元分解结果的精度，并对抗噪模型进行理论推导，证明了基于抗噪模型的混合像元分解的可行性及优越性。The present invention overcomes the influence of additive noise, multiplicative noise and mixed noise on the decomposition of hyperspectral image mixed pixels by constructing an anti-noise based mixed pixel decomposition model. This model effectively overcomes the multiplicative noise, so as to avoid mixed noise, obtain more accurate signal reconstruction, improve the accuracy of mixed pixel decomposition results, and theoretically deduce the anti-noise model, which proves the feasibility of the mixed pixel decomposition based on the anti-noise model. Superiority.
上述实施例是对本发明的说明，不是对本发明的限定，任何对本发明简单变换后的方案均属于本发明的保护范围。The above-mentioned embodiment is an illustration of the present invention, not a limitation of the present invention, and any solution after a simple transformation of the present invention belongs to the protection scope of the present invention.
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| CN102193090A (en) * | 2010-03-19 | 2011-09-21 | 复旦大学 | Mixed pixel decomposition method for remote sensing images |
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| CN101221243A (en) * | 2007-11-01 | 2008-07-16 | 复旦大学 | Mixed Pixel Decomposition Method of Remote Sensing Image Based on Non-negative Matrix Factorization |
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