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Optimized maximum noise fraction for dimensionality reduction of Chinese HJ1A hyperspectral data
EURASIP Journal on Advances in Signal Processing volume 2013, Article number: 65 (2013)
Abstract
The important techniques in processing hyperspectral data acquired by interference imaging spectrometer onboard Small Satellite Constellation for Environment and Disaster mitigation (HJ1A) are studied in this article. First, a new noise estimation method, named residualscaled local standard deviations, is used to analyze the noise condition of HJ1A hyperspectral images. Then, an optimized maximum noise fraction (OMNF) transform is proposed for dimensionality reduction of HJ1A images, which adopts an accurately estimated noise covariance matrix for noise whitening. The proposed OMNF method is less sensitive to noise distribution and interference existence, thus it can more efficiently compact useful data information in a lowdimensional space. The proposed OMNF is evaluated through two applications, i.e., spectral unmixing and classification, using the HJ1A image acquired at the Bohai Sea area in China. It demonstrates that the proposed OMNF provides better performance in comparison with other traditional dimensionality reduction methods.
1. Introduction
Hyperspectral images contain abundant spatial, spectral, and radiometric information of earth surfaces, which makes earth observation and information acquisition much more effective and efficient for some applications [1, 2]. Hyperspectral remote sensing images can be acquired through airborne or spaceborne sensors. There are two remote sensing satellites carrying hyperspectral imagers in China: the moon exploration satellite CE1 launched during 2007 and the small satellite constellation for environment and disaster mitigation (HJ1A) launched during 2008. The hyperspectral imager carried on HJ1A satellite (HJ1AHSI) is the first spaceborne hyperspectral imager in China, which is also one of few international spaceborne imaging spectrometers [3]. Instead of adopting the traditional dispersion element to acquire spectrometry, this spectrometer employs an advanced interference spectrometry technique. HJ1AHSI first acquires an interference curve for each pixel, and then uses the Fourier transform to convert interference curves to spectral curves. The interference spectrometer is modulated across space using the Sagnac interference approach. Its successful operation and application open a new era of Chinese earth observation technology. Although HJ1A has been operated for several years, new developments for HJ1A data processing are important for further research and application due to the new interference spectrometry technique used in the sensor.
In general, a hyperspectral image contains hundreds of bands with high spectral resolution, which brings about difficulty in data processing due to data redundancy and complexity. Furthermore, the special characteristic of HJ1A data (i.e., the distribution of noise and interference present in spectral and spatial domain) makes its application more difficult. Therefore, efficient dimensionality reduction remains as one of the key issues for HJ1A data processing. Principal component analysis (PCA), which is widely used for dimensionality reduction in hyperspectral image processing [4, 5], transforms raw hyperspectral data into a new feature space with mutually orthogonal coordinates. It preserves most information of original data in a lowdimensional space. However, the performance of PCA strongly depends on noise characteristics. When noise variance is larger than signal variance in one band or when the noise is not uniformly distributed between each band, PCA cannot guarantee that image quality decreases for principal components with lower ranking [6]. This drawback limits its application for hyperspectral images, which generally have very different types of noise. For example, in hyperspectral unmixing, noisy pixels might be extracted as endmembers which normally correspond to known and macroscopically pure materials.
Recently, some new approaches have been proposed to deal with noise. One of the most popular ones is the maximum noise fraction (MNF) transform [6, 7]. Similar to PCA, MNF also transforms the original data to a feature space; however, features are arranged in terms of image quality, which is measured with signaltonoise ratio (SNR). In MNF, noise covariance matrix (NCM) needs to be estimated [8–10], which is a key step. In the original MNF, only spatial information is used for NCM estimation, which may not effectively handle special noise with regular pattern, such as interference in HJ1A data.
There are many methods developed for noise estimation in image analysis [2]. Some traditional approaches use homogeneous area (HA) selection and spatial character analysis, such as HA method [11], Geostatistical method [11], and local mean and local standard deviation method [12]. However, these methods are easily affected by land cover types in the image. To solve this problem, Roger and Arnold [13] proposed Spectral and Spatial DeCorrelation (SSDC) method. Compared with traditional methods, SSDC is more stable, and is widely used. However, SSDC also has some limitations. For example, the noise estimation may be inaccurate when hyperspectral image mainly contains one earth object with absorption feature in some bands, or when the image has a specific complex texture [14]. Residualscaled Local Standard Deviations method (RLSD) [15] estimates signals according to high spectral correlation and eliminates the influence of complex texture and absorption feature by statistical analysis of subblocks. Thus, it is more stable than the SSDC and Homogeneous Regions Division and Spectral DeCorrelation method [14], especially for hyperspectral images mainly covered by water. In this article, based on the characteristics of HJ1A data, we use RLSD for SNR estimation and noise distribution analysis. Then, we propose an optimized MNF (OMNF) transform for dimensionality reduction, which contains two steps: the NCM is calculated via the SSDC, followed by the OMNF transform. Moreover, we propose an assessment framework to evaluate the performance of OMNF via spectral unmixing and classification.
The remainder of this article is organized as follows. Section 2 introduces OMNF method. Section 3 describes experimental image database, performance assessment framework, and comparative analysis methods. In Section 4, noise characteristics of HJ1A image are analyzed, and evaluation of OMNF using spectral unmixing and classification is presented. Section 5 draws conclusions.
2. OMNF transform
Let X be a hyperspectral image data, S and N are signal component and noise component contained in image data, respectively. Assume S and N are uncorrelated, then X follows a linear model:
Then, data covariance matrix can be represented as
where ∑_{ S } and ∑_{ N } are the covariance matrix of S and N, respectively. The MNF transform is expressed as
where Y is the MNF result of X, A is the MNF transform matrix. SNR of each component in Y can be analyzed as
where Var{} computes the variance, a _{ i } is the i th component in A. Then we can obtain
where Λ and A are the eigenvalue matrix and eigenvector matrix of ${\sum}_{N}^{1}\sum $, respectively. MNF is also called noiseadjusted principal components analysis which contains two steps [16, 17]. The first step is noise whitening of the hyperspectral image, then PCA is applied to noise whitened data. The main difference between conventional PCA and MNF is that MNF has a prior step of noise whitening, which needs to estimate the NCM. The original MNF method mainly adopts the spatial feature of image to estimate ∑_{ N }, such as minimum/maximum autocorrelation factor (MAF), causal simultaneous autoregressive, and quadratic surface [18]. However, as shown in some studies [8–10], spacebased noise estimation method is dataselective and unstable. This is because when hyperspectral image has low spatial resolution, the difference between pixels may mainly contain signal. Sometimes, noise with regular pattern, e.g., interference in spatial domain, may be considered as signal when only spatial features are used in noise estimation for MNF.
In hyperspectral images, correlation between bands generally is very large. Therefore, high correlations between bands can also be used for noise estimation, such as SSDC, which is a very useful method for hyperspectral noise estimation [13]. SSDC makes use of the high correlation of hyperspectral data in spatial and spectral domain together, where the radiation value of adjacent bands and pixels is used to estimate the radiation signal value of current pixel through multiple linear regression. Then the estimated radiation signal value is deducted from the actual radiation value of the current pixel, and the remaining value is considered as noise. However, since hyperspectral images do not completely meet the hypothesis adopted in SSDC, we cannot estimate the noise images following model (1). For example, there still is some correlation between noise images. Therefore, implementation of SSDC in Greco et al.’s study [9] is not feasible to estimate NCM for hyperspectral data.
2.1. NCM estimation
The most difference between MNF and OMNF is that OMNF adopts more accurate noise covariance estimation. In the proposed OMNF, noise image computed by SSDC can be used to estimate NCM. In order to control the influence of spatial feature, the image is divided into nonoverlapping small subblocks, where noise image estimated by residual of each subblock can be used to calculate NCM. SSDC adopted in this article uses multiple linear regression to estimate noise image:
where x _{ i,j,k } is the pixel value of band k at (i, j) in a certain subblock, x _{ i,j,k1} and x _{ i,j,k+1} are pixel values in band k – 1 and k + 1, x _{ p,k } is the pixel value spatially near x _{ i,j,k } in band k, a, b, c, and d are parameters which need to be estimated through multiple linear regression. In (6), x _{ p,k } is defined as
where the pixel located at (1,1) of the subblock is not considered. SSDC estimates possible signal value ${\widehat{x}}_{i,j,k}$ at band k from the obtained parameters. Then, noise of each pixel can be obtained through ${r}_{i,j,k}={x}_{i,j,k}{\widehat{x}}_{i,j,k}$. Finally, the NCM for OMNF can be calculated as follows:
where (i,j) ≠ (1,1), W, H are the width and height of image, respectively, and N is the total number of bands.
2.2. OMNF transformation
After noise variance is estimated through (8), noise correlation is removed through noise whitening with (5). Finally, dimensionality reduction can be performed through (3).
3. Experiments design and assessment methods
3.1. HJ1A hyperspectral data
The InterFerometric Imaging Spectrometer (IFIS) installed on HJ1A is the first hyperspectral earth observation sensor in China [3]. Its spectrum ranges from 0.45 to 0.95 μm with 115 spectral bands. The average spectral resolution is about 5 nm. The nominal ground sample distance is 100 m with an image swath of about 60 km. IFIS is a typical Sagnac imaging Fourier transform spectrometer featured by a compact structure, small volume, and light weight. Table 1 lists the parameters of the IFIS on HJ1A comparing to those of HYPERION on Earth Observing 1 (EO1) and Compact High Resolution Imaging Spectrometer (CHRIS) on PRoject for OnBoard Autonomy (PROBA). This hyperspectral imaging sensor has excellent specifications for practical applications. However, the data quality is degraded by severe noise. The new interferometric spectrometer technique is used in this sensor, which makes that the noise characteristics of IFIS are very different from noise contained in normal dispersion spectrometry used in HYPERION and CHRIS. For instance, regular striping noise is still present after calibration, and cannot effectively be removed by Fourier transform and notch filter method. Therefore, effective noise removal is crucial.
In this article, HJ1A images at Bohai Sea area are chosen for experiments (Figure 1). The HJ1A hyperspectral images used here contain 115 bands, and 400 × 400 pixels.
3.2. Noise characteristics analysis
Image noise may be periodic noise or random noise. Periodic noise can effectively be eliminated through frequency domain filtering, such as notch or bandpass filtering. However, it is more complex to effectively remove random noise, which is generally assumed to be additive Gaussian white noise [19, 20]. In this article, we propose to use RLSD [15] for noise estimation. In summary, RLSD procedure is described as follows:
Step 1: We divide the image into many small rectangular subblocks, and then calculate parameters a, b, and c of signal component in each subblock through multiple linear regression:
Here, x _{ k } is a vector with N × 1 values, where N = w × h with w and h being width and height of a certain subblock at band k, respectively. Then, the estimated signal value ${\widehat{x}}_{k}$ is calculated through the obtained parameters and pixel value at adjacent bands. Finally, the residuals are obtained by: $\mathbf{r}={\mathbf{x}}_{k}{\widehat{x}}_{k}$. Since the predictable signal information between bands is removed, the remained ‘unexplained’ residuals can approximate noise.
Step 2: The Local Standard Deviation (LSD) is calculated at each subblock as follows:
where M is the number of pixels of this subblock and S ^{2} is the variance of residuals of the subblock. As there are three parameters used in multiple linear regression shown in (9), the unbiased estimation requires the term of M – 3.
Step 3: After LSDs of all subblocks are calculated, we extract maximum and minimum values of the obtained LSDs. Then, several bins with equal interval are set between these two values. The numbers of subblocks in each bin can be counted according to its LSD value. Finally, the mean LSD value of the bin with the most number of blocks is calculated, which can be considered as the noise of the whole image.
3.3. Assessment framework and methods
We consider several dimensionality reduction methods, i.e., PCA, MAF, MNF, and OMNF, for evaluation. Since the spatial resolution of HJ1A hyperspectral data is 100 m, mixed pixels generally exist in the image. Therefore, we consider spectral unmixing for evaluation from fullpixel scale to subpixel scale. Similarly, image classification is also considered for evaluation as it has important applications. Figure 2 shows the flowchart of the proposed scheme.
3.3.1. Spectral unmixing method
Spectral unmixing mainly obtains endmember extraction and abundance estimation [21, 22]. Endmember extraction extracts pure pixels. Abundance estimation estimates the proportion of each endmember in a mixed pixel. In spectral unmixing, abundance estimation generally adopts a least squares method (constrained or unconstrained). Many endmember extraction methods are developed, such as, Pixel Purity Index (PPI), NFINDR, Vertex Component Analysis (VCA), Iterative Error Analysis (IEA), and so on [22].
In the aforementioned methods, NFINDR is one of the most widely used algorithms [23]. Its aim is to find a set of pixels that can construct a simplex with the maximum volume. These pixels can be considered as endmembers. Due to the requirement of a square matrix used in volume calculation in NFINDR, the original image must be transformed to a (p – 1)dimensional subspace by a dimensionality reduction method.
3.3.2. Image classification method
Hyperspectral classification can be supervised or unsupervised, parametric or nonparametric, and hard or soft (fuzzy). Traditional pixelbased classification methods, such as Maximum Likelihood Classifier (MLC), Spectral Angle Mapper (SAM), Minimum Distance Classifier (MDC), analyze data without incorporating spatial information. However, spatial information can play an important role in hyperspectral image classification [24]. Classification accuracy can greatly be improved when spatial and spectral features are effectively combined [25]. In this study, we propose to use a Homogenous Objects Extraction (HOE)based method to combine spectral and spatial information for classification. Meanwhile, the HOE method can efficiently deal with the special noise present in HJ1A data.
In homogenous objectoriented image classification, such as HOE, the key issue is to extract the objects with high homogeneity. Nonuniform radiation response increases spectral variation, which is common with the high degree of spectral heterogeneity in complex landscape. Thus, in the HOEbased classification approach used in this study, all pixels inside a homogeneous object can be considered belonging to the same class. Furthermore, since homogeneous regions are extracted through spectral similarity between pixel and neighborhoods, integration of spectral feature and a series of spatial features (such as shape, size, texture, and context relationship) can be applied in classification. This approach mainly includes three steps: image segmentation, feature extraction, and classification.
Image segmentation
In this article, fuzzy Kmeans clustering is used for image segmentation. Fuzzy Kmeans is a soft clustering algorithm which determines the subordination degree of each pixel in each type according to that of its vector value between [0, 1]. This algorithm is an iterative process, where each type of centroids (ci) and pixel subordination matrix (uij) are adjusted using (11) until the convergence of objection function $J={\displaystyle \sum _{i=1}^{k}{\displaystyle \sum _{j=1}^{n}{u}_{\mathit{ij}}^{m}{d}_{\mathit{ij}}^{2}}}$.
where m∈[1, ∞] is a weighted index, d _{ ij } is dissimilarity measurement, such as Euclidean distance.
Feature extraction
After image segmentation, the features of homogeneous objects can be extracted, which may include the spatial position, spectra of the homogenous object, and its class label. Since all the pixels in the same segment belong to the same class, the class label of the segment can be obtained by tracking the margin through a contourbased object tracking method. Moreover, the mean spectrum of all pixels in each homogeneous object is used as the spectral feature for this object.
Classification
In general, traditional pixelbased method performs classification by comparing the spectral similarity of each pixel with prior knowledge of the training samples. In the HOEbased method, pixelwise training samples need to be transformed to objects according to the relationship between a given pixel and its corresponding homogenous object. Such classification model parameters can be estimated by training the objects at different homogeneous regions. As shown in (12), the Mahalanobis Distance (MD) is considered:
where z _{ l } and ∑ _{ l } are the mean vector and covariance matrix of training samples, respectively.
4. Experiments and results analysis
4.1. Noise characteristics analysis of HJ1A hyperspectral data
The diagnostic spectral features of earth materials are required for image classification and information extraction of hyperspectral images. However, hyperspectral sensor acquires data with very small spectral interval. Thus, there is insufficient optical energy for each band. It is much more difficult to improve SNR of hyperspectral data than panchromatic or multispectral images. Absorption feature of the spectrum can be detected only when spectral absorption depth is one magnitude greater than the noise level [26]. During data acquisition, the spectral feature of earth object, however, is easily distorted by noise.
In this study, the size of each subblock is 8 × 8 pixels. In order to handle the interval bin division (see step 3 in the RLSD procedure), we estimate the noise based on the parameters estimated by the technique proposed in [12], where the bins are set in the range between the minimum LSD and 1.2 times of LSD mean value, and 150 bins are recommended.
Figure 3 illustrates some bands of the considered HJ1A data at Bohai Sea area. It is noticeable that image quality of these bands is significantly different. This is reasonable, since, according to the interference device used in HJ1A sensor, spectral information is acquired in a way different from the dispersive spectrometer. It receives interference data modulated and interfered by target spectral information. The ordinary data with spectral radiation information can be obtained through spectral restoration. For the errors produced by interference device and spectral restoration, HJ1A hyperspectral data are disturbed with periodical strip at spatial domain, which is difficult to be eliminated by traditional radiance calibration methods [3]. Therefore, in order to guarantee the precision and accuracy of image classification and spectral unmixing, this special noise requires specific method to remove.
Figure 4 shows the SNR estimates from RLSD. It can be observed that noise distribution is nonuniform. Furthermore, it is well known that noise condition is more realistic when the image mainly covers water area [27]. Therefore, dimensionality reduction with effective noiseelimination is important for real applications.
4.2. Dimensionality reduction results
Figure 5 shows the six components of the considered dimensionality reduction methods. It can be seen that the first two components obtained from PCA (see Figure 5a) have most information of the data. However, it is possible that these principle components contain noise which is nonuniformly distributed in the spectral domain. Therefore, PCA is not well suitable for dimensionality reduction of HJ1A data. Furthermore, as shown in Figure 5b, the first three components of MAF have most spatial correlations of the image, which means those components have most volume of the signal. The fourth and fifth components are almost noise. However, the sixth component contains information. This brings difficulty for determining the number of components. Therefore, MAF is also not suitable for dimensionality reduction of HJ1A hyperspectral images. Moreover, Figure 5c shows the components obtained from MNF. It can be seen that the first two components also have the highest image quality. However, the fifth component contains more information than the third and fourth components, which are interfered by periodic strips. Thus, although traditional MNF takes noise into account and can solve the influence of nonuniform noise distribution in spectral domain, it is easily affected by the hybrid distributions of earth objects and periodic interference; thus, its components may not be arranged in descending order of image quality. Finally, Figure 5d shows the components obtained by the proposed OMNF method. It can be observed that OMNF reduces data dimensionality more effectively where all components are arranged in descending order of image quality.
4.3. Comparative performance analysis
In this section, the first three components of PCA, MAF, and OMNF are used for spectral unmixing and image classification, and the first, second, and fifth components of traditional MNF are used for spectral unmixing and image classification.
4.3.1. Spectral unmixing
Endmember extraction and abundance estimation by NFINDR and unconstrained least squares methods are applied to the dimensionalityreduced data obtained from PCA, MAF, MNF, and OMNF. Based on the obtained components, only four endmembers are extracted, and Figure 6 shows the obtained abundance and error maps. Several conclusions can be obtained from Figure 6. First of all, the results obtained from the PCA components are only the salt area is appropriate and all the other endmembers are greatly affected by noise. Furthermore, it can be seen that the results obtained from MAF, MNF, and OMNF components are better than those of PCA, where OMNF obtains the best results. This is because all these methods take noise into account. Moreover, it can be observed that the abundance estimations of vegetation, salt area, muddy water, and water body are more reasonable in geographical distribution than results from other dimensionality reduction methods. This is because OMNF eliminates noise during the dimensionality reduction procedure. For example, distribution of vegetation in abundance map of OMNF is better than others. Another example is distribution of salt area is repeated in the abundance maps of salt area and water body in both MAF and MNF results.
4.3.2. Image classification
Figure 7 shows the reference data on the false color composite. In the dataset, 20% of samples are used for training, and the rest for testing. Training and testing samples were randomly selected from the reference data.
Figure 8 shows the classification results obtained from the raw data, the dimensionalityreduced data from the MNF and OMNF, respectively. It can be seen that the pixelbased classification using OMNF features obtained the best result, especially for the water and sea beach classes.
Figures 9 and 10 illustrate the classification results obtained from the MNF and OMNF features by the HOE method, respectively. Figures 9a and 10a present the segmentation of the hyperspectral image. Two steps are involved in this process. The first step is the fuzzy Kmeans clustering, followed by edge tracking to obtain the boundaries of the ground objects in the second step. As can be seen from Figures 9b and 10b, the classification results are better than those in Figure 8. Overall, classification result using OMNF and HOE is the best.
The producer’s accuracy is used for further assessment [28]. Figure 11 shows the classification accuracies, where five methods are considered: pixelbased classification on the raw data, pixelbased classification on reduced data from MNF, pixelbased classification on reduced data from OMNF, HOEbased classification on reduced data from MNF, and HOEbased classification on reduced data from OMNF. It can be observed that HOEbased classification is better than the pixelbased method for water body in most parts of the study area (including water in sea water and salt area in saltern) and for sea beach, vegetation, and salt area in saltern. The obtained Kappa coefficients are 0.4076, 0.6229, 0.6740, 0.7011, and 0.8704 for pixelbased classification on the raw data, pixelbased classification of the MNFreduced data, pixelbased classification of the OMNFreduced data, HOEbased classification of the MNFreduced data, and HOEbased classification of the OMNFreduced data, respectively. It can be seen that the proposed HOE with OMNF method leads to excellent classification performance, which produced the highest accuracy for the considered HJ1A hyperspectral image.
5. Conclusion and discussion
Hyperspectral imager carried on HJ1A satellite indicates a new development stage of hyperspectral remote sensing technology in China. However, due to the new interference spectrometry technique implemented in this sensor, noise characteristics of HJ1A images are more complex than images acquired by other hyperspectral sensors, such as HYPERION and CHRIS. This article presents an OMNF method for dimensionality reduction for HJ1A images, which estimates the NCM using SSDC method. The proposed approach is evaluated by a real HJ1A hyperspectral data at Bohai Sea. Both unmixing and classification results indicate that the proposed method can offer excellent performance for HJ1A data applications.
Abbreviations
 HJ1A:

Small satellite constellation for environment and disaster mitigation
 HOE:

Homogenous objects extractionbased method
 IFIS:

Interferometric imaging spectrometer
 LSD:

Local standard deviation
 MAF:

Minimum/maximum autocorrelation factor
 MD:

Mahalanobis distance
 MNF:

Maximum noise fraction
 NCM:

Noise covariance matrix
 OMNF:

Optimized maximum noise fraction transformation
 PCA:

Principal component analysis
 RLSD:

Residualscaled local standard deviations method
 SNR:

Signaltonoise ratio
 SSDC:

Spectral and spatial decorrelation method.
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Acknowledgements
This research was supported by the National Natural Science Foundation of China under Grants nos. 40901225 and 41201356, and by the National High Technology Research and Development Program of China (863) under Grant no. 2011AA120203. The authors would like to express their gratitude to the anonymous reviewers for their detailed comments that improved both the editorial and technical quality of this article substantially.
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Gao, L., Zhang, B., Sun, X. et al. Optimized maximum noise fraction for dimensionality reduction of Chinese HJ1A hyperspectral data. EURASIP J. Adv. Signal Process. 2013, 65 (2013). https://doi.org/10.1186/16876180201365
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Keywords
 Hyperspectral image
 Dimensionality reduction
 Maximum noise fraction transform
 Noise estimation
 Classification
 Spectral unmixing