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2Centre for Excellence in Networking, Amrita Vishwa Vidyapeetham. Coimbatore–641 112, India. *[email protected]. Abstract: In this paper, we present ...
An Effective Pre-processing Algorithm for Detecting Noisy Spectral Bands in Hyperspectral Imagery D. Bharath Bhushan1, V. Sowmya2, M. Sabarimalai Manikandan2* and K.P. Soman2 1

2

Indian Institute of Space Science and Technology, Trivandrum–695 547, India Centre for Excellence in Networking, Amrita Vishwa Vidyapeetham. Coimbatore–641 112, India *[email protected]

Abstract: In this paper, we present an effective pre-processing algorithm for band selection approach which is an essential task in hyperspectral image analysis. The pre-processing algorithm is developed based on the average inter-band block-wise correlation coefficient measure and a simple thresholding strategy. Here, the threshold parameter is found based on the standard deviation of the average inter-band block-wise correlation coefficients. The performance of the proposed algorithm is validated using the standard hyperspectral database created by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) sensor. By comparing the detected bands with ground-truth annotations, we observed that the proposed algorithm identifies the noisy and water absorption bands in the high-dimensional hyperspectral images. The proposed algorithm achieves the classification accuracy of 94.73%. Keywords: Hyperspectral Imagery, Noisy Spectral Bands, Thresholding, Inter-band Correlation Coefficient.

1. Introduction Hyperspectral image analysis plays an important role in various remote sensing applications such as objects detection and classification, mineral processing and disease detection [1]–[12]. Imaging spectrometry is an approach to Earth imaging, which is developed to measure, analysis, and interpret spectra information acquired from a specific object at a short, medium or long distance. In most of the applications, 34 978-1-4673-0266-1/11/$26.00 ©2011 IEEE

hyperspectral sensor is used to collect a large number of spectral bands with a fine spatial resolution in order to improve the classification accuracy. For example, the Airborne Visible Infrared Imaging Spectrometer (AVIRIS) system is was the first imaging spectrometer to measure the solar reflected spectrum from 400 nm to 2500 nm at nominal spectral resolution of 10 nm that finally provides 224 contiguous spectral bands [1]. The AVIRIS spectral image dataset contains noisy spectral bands (band 1–5 Proceedings of SYMPOL-2011

and 215–220) and water absorption bands (band 103–113 and 148–164). More generally, the hyperspectral imagery (HIS) is available in very high-dimensional space. In such cases, complexity of the hyperspectral image processing

techniques heavily relies on the following factors: i) the number of spectral bands; ii) the size of the spectral band; and iii) the number of discriminatively informative bands. In many situations, the hyperspectral imagery includes

Fig. 1: Noisy Spectral Bands Extracted from AVIRIS Dataset

Fig. 2: Informative Spectral Bands Extracted from AVIRIS Dataset

less informative bands (or band with low signal to noise ratio (SNR)), noisy and water absorption bands. Figs. 1 and 2 show some of noisy bands and informative bands of AVIRIS hyperspectral dataset respectively. By exploiting the characteristics of spectral bands, the less informative and noisy bands can be removed before performing the HSI analysis. The removal of these spectral bands may increase the classification accuracy and also decrease memory space and transmission bandwidth requirements. Therefore, many researchers have reported various band-selection approaches for dimensionality reduction. In this paper, we introduce a simple and effective preprocessing algorithm to improve the efficiency of band-selection method. The pre-processing algorithm automatically detects noisy and water absorption bands in high dimensional data. The rest of this paper is organized as follows. The mathematical background involved in the proposed algorithm is described in Section 2. The results of the proposed work are discussed in Section 3. The performance of the algorithm is also summarized with the benchmark parameters. Finally, conclusions are drawn in Section 4.

2. Materials and Methods In this Section, we describe the proposed algorithm. The pre-processing algorithm consists of four steps: i) Zero Padding and Blocking, ii) Inter-band block-wise correlation coefficient, iii) Standard deviation of correlation coefficient vector, iv) Smoothing and Thresholding.

2.1 Zero Padding and Blocking Let X denotes the HSI of size m × n × k , where m, n, k are the number of scanning lines, number of pixels in the scan line and number of bands in HSI respectively. The hyperspectral bands are separated into blocks in order to find the local measures of successive bands in HSI. Each band of HSI is divided into blocks with size of p × p . The hyperspectral image is padded with number of zeros in row and column according to the equation (1). Now, the size of hyperspectral image X becomes ( m + r ) × ( n + c ) × k . The size of blocks across the rows and columns are given by:

D. Bharath Bhushan et al.: An Effective Pre-processing Algorithm for Detecting Noisy…

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… (1)

The standard deviation is computed using the inter-band correlation coefficient matrix ρ. The

Bi be the p × p blocks in the j th band and

standard deviation of j and (j + 1) band correlation coefficient is expressed below as:

r = p-mod(m,p) c = p-mod(n,p) Let

Bi ' be the

p× p

in

the

th

(j + 1) band

respectively.

σj =

2.2 Inter-band Block-wise Correlation Based Features To detect the existence of the noisy spectral bands, inter-band block-wise correlation-based feature extraction algorithm is proposed in this work. The inter-band cross correlation coefficient is calculated between the each block th

th

of the j and (j + 1) bands of HSI respectively. It measures the local spatial correlation between successive bands. Let bi

bi ' be the 1-D version of Bi and Bi ' respectively. The correlation coefficient of bi and bi ' is described by the equation as and

ρ

ji

=

n(biTbi ')−((eTbi )(eTbi ')) T T 2 T T 2 [n(bi bi )−(e bi ) ] −[n(bi ' bi ')−(e bi ' )] 1 ≤ j ≤ k −1

1 ≤ i ≤ M× N

… (2) where n is total number of pixels in a block and T e = [1,1,1,1…..] is the vector containing all ones. The size of e, bi , bi ' , n are p2 x 1. Here j

denotes the band number in the HSI and i denotes the block number for a band j. For each j, i vary from 1 to total number of blocks in each band. ρ is the column vector containing ji inter-band correlation coefficient of all blocks th

th

th

of j and (j + 1) band, respectively. The correlation matrix of all the blocks between two successive spectral bands is expressed as: ρ = [ ρ1i, ρ 2i, ..........., ρ (k −1)i ]

… (3)

1 N

th

T (ρ ji − μ j ) − (ρ ji − μ j ) … (4)

1 ≤ j≤ k − 1 where N is the total no of blocks, for each j, i takes all the values. So for each j, ρji is the column vector of correlation coefficient of all blocks in j

th

th

and (j + 1) band and μ j is the th

th

mean of the j and (j + 1) band inter-band correlation coefficient. Finally, the standard deviations vector is given as: σ = [σ1, σ 2, ..........., σ(k −1) ]

… (5)

σ1 is the standard deviation of inter band block-wise correlation coefficients obtained for the spectral band number 1.

2.3 Detecting Noisy Bands In this step, the noisy spectral bands are automatically detected based on a simple thresholding rule with an adaptive threshold. The optimal threshold η is determined based on the standard deviation of inter band correlation coefficient σ that is computed as:

η=

K −1 2 ∑ ( σi − μ ) K − 1 k =1 1

… (6)

where K denotes the number of spectral bands in HSI data. From the experiment on HSI datasets, it is observed that the noisy bands have higher standard deviation value of ρ. An optimal threshold η is determined such that it eliminates most of the noisy bands in HSI. Fig. 3 shows the plot of standard deviation of inter-band correlation coefficient for all the hyperspectral bands in the standard dataset. The dotted line in the plot represents the threshold

D. Bharath Bhushan et al.: An Effective Pre-processing Algorithm for Detecting Noisy…

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for the standard hyperspectral dataset. The hard thresholding function is defined as:

Bk =

{

1, σ k > η 0, otherwise

… (7)

The correlation features are set to zero if the value of σ k > η , for k = 1, 2…. K–1. This process results in binary vector B. The zeros in the binary vector indicate the noisy spectral bands and ones indicate the informative bands. The noisy spectral bands are marked that will be eliminated from the classification task.

3. Results and Discussion In order to evaluate the effectiveness of the proposed pre-processing algorithm, we used the standard hyperspectral AVIRIS datasets and computed the benchmark parameters for testing and comparison purposes. In the ground truth annotation, the noisy bands, water absorption bands and the spectral bands with low SNR are considered as noisy class and the spectral bands with high SNR are considered as informative class. Since the presence of noisy bands reduces the accuracy and increases complexity of classification algorithm, noisy bands were removed manually in the literature. But manual process is tedious and time consuming. Thus, the method is required for automatically eliminating the noisy and less informative bands. In this work, the calculation of inter-band correlation coefficient is performed with various block sizes and 32 × 32 is determined as the optimal block size. In order to make the size of HSI m × n exactly divisible by bock size p, the matrix is padded with zeros in row-wise and column-wise. Then, the correlation coefficient is computed between the blocks of the successive bands. Finally, we obtain M × N correlation coefficients for each pair of successive spectral bands. The standard deviation is determined for the correlation coefficients vector ρ. The experiment on the above datasets shows that the noisy bands have high standard deviation of inter-band correlation coefficient. The threshold

value is automatically determined based on the standard deviation of inter-band correlation coefficient. The standard deviations for all the spectral bands from AVIRIS data are plotted in Fig. 3. The threshold line is also plotted as the dotted straight line and the noisy bands are marked in Figure 3 the spectral bands with standard deviations which are above the threshold line are classified to the noisy and water absorption bands. Fig. 4 illustrates that the noisy bands for AVIRIS dataset lies in the region 1–4, 35, 103–111, 148–164 and 213–220. By visual analysis, these bands are interpreted as low grade noisy bands shown in Fig. 4 illustrates that the proposed method provides the better way to discard the noisy and water absorption bands. In this work, the three probabilities such as probability of correctly detecting noisy bands ( Pcn ), probability of correctly detecting informative bands ( Pci ), and probability falsely detecting bands ( Pf ) are computed for evaluation purposes: N Pcn (%) = cn × 100 Ngn Pci (%) =

Nci × 100 Ngi

Pf (%) =

Nf × 100 N

… (7)

where Ncn is the total number of correctly detected noisy bands, Ngn is the total number of noisy bands in ground truth annotation, Nci is the total number of correctly detected informative bands, Ngi is the total number of informative bands in ground truth annotation, Nf is the total number of falsely detected bands and N is the total number of bands in ground truth annotation. The experimental results of the proposed algorithm are shown in Table 1. From the table, it can be observed that in terms of the noisy, correct and false detection probabilities, the proposed pre-processing algorithm is significantly has lower probability of false detection and a higher probability of correct informative band

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detection. The proposed algorithm has the probabilities of correctly detecting informative and noisy bands of 97.25% and 94.73%, respectively. The algorithm has the probability of falsely detecting spectral bands of 3.18%. The noisy bands detected by the proposed algorithm are compared with noisy bands reported that

are marked manually in the literature. Hence, experiments show that the proposed algorithm can eliminate the noisy and low signal-to-noise ratio (SNR) bands and also increases the effectiveness of the Hyperspectral image classification algorithms.

Fig. 3: The standard deviations of inter-band block-wise correlation coefficients obtained for pair of successive spectral bands from the AVIRIS dataset

Table 1: Performance of the Proposed Algorithm Total Number of Bands

Number of Noisy Bands

Number of Informati ve Bands

Number of Correctly Detected Noisy Bands

Number of Correctly Detected Informative Bands

Number of Falsely Detected Bands

Pcn (%)

Pci (%)

Pf (%)

220

38

182

36

177

7

94.73

97.25

3.18

Fig. 4: Eliminated Noisy Spectral Bands from the AVIRIS Dataset by Proposed Pre-processing Algorithm

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4. Conclusion In this paper, we introduced a new pre-processing algorithm for detecting noisy bands in Hyperspectral imagery. The visual inspection of the noisy bands detected by the proposed preprocessing algorithm shows that it has very high potential in extracting informative independent bands and in eliminating the irrelevant noisy bands effectively. The spectral bands selected by this algorithm are expected to have better classification results in the HSI analysis algorithms. The proposed method achieves the probability of correctly detecting noisy bands of 94.73% and the probability of falsely detecting noisy bands of 3.18%. Based on the observation, the advantages of the proposed pre-processing algorithm are summarized: i) it eliminates the noisy bands, ii) it provides the better quality bands for HSI analysis, and iii) it reduces the computation complexity of band selection approach.

[5] Bajcsy, Peter and Groves, Peter, “Methodology for hyperspectral band selection,” Photogrammetric Engineering and Remote sensing, vol. 70, no. 7, pp. 793–802, July 2004. [6] Guo, Baofeng, Gunn, Steve R., Damper, R.I. and Nelson, J.D.B., “Band Selection for

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