Denoising Cloud Interference on Landsat Satellite Image Using Discrete Haar Wavelet Transformation

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Denoising Cloud Interference on Landsat Satellite Image Using Discrete Haar Wavelet Transformation Powered By Docstoc
					                                                                (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                Vol. 10, No. 1, January 2012

   Denoising Cloud Interference on Landsat Satellite
  Image Using Discrete Haar Wavelet Transformation

            Candra Dewi                               Mega Satya Ciptaningrum                                   Muh Arif Rahman
     Department of Mathematic                          Department of Mathematic                             Department of Mathematic
      University of Brawijaya                           University of Brawijaya                              University of Brawijaya
        Malang, Indonesia                                 Malang, Indonesia                                    Malang, Indonesia                                             

Abstract—Satellite imagery is very useful in information                    that is performed by Choi and Bindschadler (2004), clouds is
acquisition of the earth's surface image, especially the earth's            very high reflected in the band 2 (0.52 - 0.60 µm).
resources. However, in the process of retrieval information from
satellite imagery is often found barriers that can obscure or even              The elimination process of noise in the spatial domain can
cover the imaging of an area. One of these barriers is a cloud,             be applied directly on image pixels. One of the transformation
which result the image that covered with lots of noise. Wavelet             methods that can be done on the spatial domain is a power-law
transformation was usually used to enhance the image or to                  transformation. While in the frequency domain, the image is
eliminate striping noise on satellite image. In this paper is used          broken into multiple kernels to be processed by the analysis of
Discrete Haar Wavelet transformation to reduce cloud noise on               transformation. Transformations that can be done in this
Landsat TM image. The process includes the Haar Wavelet                     domain include Wavelet transformation [3] [4] [5].
decomposition of image rows and columns. After that,                        Transformation performed to obtain information and identify
thresholding process is also applied for de-noising. Thresholding           the original image, by getting its spectrum. Spectrum can be
results are then reconstructed using the Inverse Discrete Haar              obtained from the image frequency, time, or time-frequency
Wavelet. The method is applied to the variation of the band                 depend on the type of transformation used [6].
image, the type of thresholding (hard and soft), as well as the size
of the image convolution. The testing results on the band 1 to                  It is well known that wavelet transform is a signal
band 6 of Landsat TM imagery showed that the lowest error                   processing technique which can display the signals on in both
values are calculated by RMSE (Root Mean Square Error)                      time and frequency domain. Wavelet transform is superior
present in band 1. Image signal to noise ratio in band 1 has the            approach to other time-frequency analysis tools because its
highest value, which means most high-power image signal to                  time scale width of the window can be stretched to match the
noise. This mean that band 1 has the highest pixel value                    original signal, especially in image processing studies.
similarity between whole testing data.
                                                                                Wavelet transformation can be used to obtain signal both in
   Keywords; Discrete Haar Wavelet, thresholding, image                     the frequency domain and time domain. Wavelet time scale
convolution, Landsat TM                                                     width of the window can be stretched to match the original
                                                                            signal. Wavelet is a conversion function that can be used to
                                                                            break up a function or a signal into different frequency
                                                                            components. These components then can be processed in
                       I.    INTRODUCTION                                   accordance with the scale. While the wave is a function of
   Image of the earth surface recording can be interpreted by               moving up and down in space and time periodically
the user for the benefit of various fields. In the process of               (sinusoidal), wavelet is a limited wave or sometimes is called
image acquisition by the satellite, sometimes is found noise that           as short wave [7].
can reduce the image quality. This disorder is caused by the                   Haar transform uses the Haar scaling function and the Haar
presence of such clouds or fog that can obscure or even                     wavelet function. Haar wavelet transformation use the Haar
covered the satellite during the imaging process [1]. This noise            basis functions that is called a wavelet orthonormal [8]. Haar
can interfere the interpretation process therefore the results              Wavelet functions can be expressed in matrix form.
obtained will not be maximal.
                                                                                In the previous study, wavelet transform is used to sharpen
   Each pixel in the satellite image has some digital value                 the cloud-related shadow areas [1]. Beaulieu et al (2003) refine
(numeric) in accordance with the band of satellite imagery. For             the resolution of a multi-spectral (MS) image using fusion
example is Landsat TM image that has 7 bands. Therefore,                    method and the Stationary Wavelet Transform. In the study
each pixel has 7 digital values that are suited to 7 band digital           performed by Torres and Infante (2001), wavelet transform is
value that is owned. The different characteristic each bands                used for denoising stripping noise on satellite imagery. This
causes the difference in the ability to detect clouds. In the study

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                                                             (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                             Vol. 10, No. 1, January 2012
paper applies the Haar wavelet transformation to reduce the                                 III.   RESEARCH METHOD
noise cloud on Landsat TM imagery.                                           This application was built to reduce noise on Landsat TM
                                                                         satellite image using Haar wavelet transformation method. The
                 II.   PREVIOUS RESEARCH                                 limitation of this system includes:
    The research about the using of wavelet transformation has             1) The image used is a grayscale image of type TIFF
been done by some researcher. Torres and Infante (2001)
                                                                           2) The size of the image used is 256x256 orthonormal
present new destriping technique on satellite imagery using
Daubechies wavelets of different orders and was tested on a
heavily striped Landsat MSS image. Visual inspection and                     The flowchart of noise reduction process is shown Figure 1.
measurement the signal-to-noise ratio showed that the method             The inputs of this application consist of satellite imagery with
proved produce encouraging results in image quality and                  clouds noise and image without noise. This input image is
performance, overcome some problems commonly found on                    presented in grayscale values. Some preprocessing was done to
traditional destriping techniques and reduce computer time               the noise image to reduce the noise. The image without noise is
process and storage space.                                               used as a comparison in the testing process.
    Beaulieu et al, (2003) refine the resolution of a multi-
spectral (MS) image by fusion method using a high-resolution
panchromatic (PAN) image and the Stationary Wavelet
Transform (SWT). They propose to produce high-resolution
MS image that has nearly the same statistical properties than
the original multi-spectral image with no blocking image
artifacts. These algorithms are based on the injection of high-
frequency components from the PAN image into the MS
image. They prove that pixel-level fusion was a powerful
method to refine the spatial resolution of PAN images.
    Wang et al (2003) present a new approach to eliminate the
random image noises inherent in the microarray image
processing procedure using stationary wavelet transform
(SWT) and applied on analysis of gene expression. The testing
result on sample microarray images has shown an enhanced
image quality. The results also show that it has a superior
performance than conventional discrete wavelet transform and
widely used adaptive Wiener filter in this procedure.
    Elrahman and Elhabiby (2008) developed image sharpening
algorithm using wavelet to enhance shadow areas of cloud and
tested this algorithm on the panchromatic band of Landsat 7
                                                                                       Figure 1 Flowchart of noise reduction process
ETM satellite sub-scenes. The algorithm is applied locally by
boosting the image high frequency content in the shadow areas
using the defected image de-noised wavelet coefficients. By                  Firstly, noise image is transformed into the frequency
using visual and quantitative analysis was found that the ability        domain using the Haar wavelet transform. The quantization
to enhance details under shadow areas increased with the                 process is then performed using a specific threshold value. The
increase in the number of wavelet decomposition levels.                  transformation process is performed to the n level, where N =
Beside, were found that enhancing image quality in the shadow            2n and N is the size of the image. At each level, the row
areas could be done using only two or three wavelet                      transformation is done in advance through highpass and
decomposition levels.                                                    lowpass filters. After that, is done transformation of the
    In these previous studies, the using of wavelets on the
satellite image is to sharpen the image and to improve image                 The next process is tresholding. This process separates
resolution. Wang et al (2003) already used wavelet to eliminate          pixels based on the degree of grey level values. The wavelet
the noise, but is applied to the gene sequence image. In this            coefficients which are below the threshold are set to zero and
paper will be applied discrete Haar wavelet to reduce noise in           than take the other values for purposes of reconstruction of the
the form of clouds on satellite images. Although the discrete            signal. Threshold used is Hard and Soft Threshold. With ε is
wavelet transform has a lower performance of the stationary              the threshold value, hard thresh equation is shown in (1).
wavelet transform, but its ability to reduce the noise is quite
high and does not vary with stationary wavelet transform [5].                              x, | x |> ε
                                                                            Thard ( X ) =                                              (1)
                                                                                           0 | x |≤ ε
                                                                                 On the hard threshold, all wavelet coefficients with a
                                                                         value below a specified threshold are classified as noise and
                                                                         removed (are set to zero). While the coefficients above the

                                                                                                      ISSN 1947-5500
                                                                    (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                    Vol. 10, No. 1, January 2012
threshold is classified as signal. In soft thresholding, the                 B. Peak-to-Signal Noise Ratio (PNSR)
wavelet coefficients with a value below the specified threshold                    PSNR is the comparison between the maximum possible
are removed and the wavelet coefficients above the specified                 signal strength of a digital signal with the power of noise that
threshold are reduced by the threshold value. Thus, this method
                                                                             affects on the signal (Alfatwa, 2005). PSNR is defined through
reduces the range of wavelet coefficients and signal leveling.
                                                                             the signal-to-noise ratio (SNR) to measure the level of signal
Soft threshold was chosen because this procedure does not
cause non-continuants at x = ± ε. The equation for the soft                  quality. Signal quality is directly proportional to the value of
threshold is shown in (2).                                                   SNR. The larger of the SNR value, the better the quality of the
                                                                             generated signal. PSNR values usually range between 20 and
                 sign( x)(| x | −thresh), | x |≥ ε                          40 dB (Alfatwa, 2005). PSNR values can be calculated using
   Tsoft ( X ) =                                             (2)
                            0, | x |< ε                                     equation as shown in (6). Value of 255 represents the upper
                                                                             limit value of image pixels.
    For the determination of threshold values is used equation                                      255 
as in (3).                                                                       PSNR = 20 log10                                  (6)
                                                                                                    RMSE 
          2σ 2 log(n)
    t=                                                        (3)
               n                                                                                 V.   SOURCE OF DATA
          t            = threshold value that is calculated                      Image that is used in the testing process is Landsat TM
                       = the variance of data                                satellite image with each channel has a different sensitivity to
          n            = number of data                                      the wavelength. Landsat TM satellite orbital period for taking
                                                                             pictures of the earth's surface is generally performed at least 6
                                                                             months. Satellite imagery from two period of taken picture can
   The equation of variance is shown in (4).                                 be used as a reference on the interpretation process. For
                                                                             example, this study used two images with the same object (the
   σ2 =
          ∑ (x   i   − x) 2
                                                              (4)            island of Madura) taken in June 2004 and February 2005. In
              (n − 1)                                                        the image taken on 2005 exists cloud covering the particular
                                                                             object and the image taken on 2004 (with the same object) is
    The last process is the Inverse Haar Wavelet Transform                   used as reference.
(IHWT) which is the process of passing the image through the
inverse filter matrix transformations. This process is contrary to               Preparation of satellite imagery should be done to obtain
the decomposition process.                                                   the image that is suited to analysis. The original image is
                                                                             cropped to the size of 256 x 256 pixels and converted into Tif
                       IV.    TESTING METHOD                                 extention format. In addition, the original image with 7 bands is
                                                                             separated per-band for used in applications. Details of the data
                                                                             used are as follows:
   For testing the result is used Root Mean Square Error
(RMSE) and Peak-to-Signal Noise Ratio (PNSR).                                  1) Landsat image of Madura island, dated June 25, 2004
                                                                             and dated February 4, 2005
A. Root Mean Square Error (RMSE)                                               2) Landsat image of Java island, dated June 25, 2004 and
     RMSE is one of the ways to measure the amount of the                    dated February 4, 2005
difference between the estimated values with actual values by
measuring the average of error. RMSE is calculated by                            Of the two sources of image data was made 2 pieces of
comparing the number of errors between the denoising image                   testing data with each of the data contained six band image data
and the original image. The lower the RMSE value the smaller                 (bands 1 to 6 / 7) with each size is 256 x 256 pixels.
the error calculation has been done. RMSE of digital image                      Data I: latitude 7:7:45.66 S and longitude 113:3:12. 43 E
with size NxM could be calculated using equation as shown in
(5).                                                                            Data II: latitude 7:39:41.99 S and longitude 112:56:41.87 E

    RMSE =
                 ∑ [ f (i, j ) − F (i, j )]   2
                                                              (5)                          VI.   RESULT AND DISCUSSION
   Where:                                                                        Some examples of images resulted from denoising process
                                                                             are visually displayed in Table I. The first image shows the
          f(i,j) is pixel value in original image                            result of denoising on data I (band 1) with convolution 2 (hard
          F(i,j) is the pixel value on reconstruction image                  thresholding), the second on data II (band 1) with convolution
          N2 is an image size (in pixels)                                    8 (soft thresholding), and the third on data II (band 3) with
                                                                             convolution 8 (hard thresholding).

                                                                                                       ISSN 1947-5500
                                                                          (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                          Vol. 10, No. 1, January 2012
                                                                                                            CONVOLUTION 8 (DATA II)
  No     Band             Input Images              Output Images
                                                                                              Thresh              RMSE                      PNSR
                                                                                     Band                   Hard       Soft           Hard       Soft
                                                                                                          Threshold  Threshold      Threshold  Threshold
                                                                                       1        2,96          7,422        7,041        30,72          31,178
  1     (data I)
                                                                                       2        2,46         10,339        9,863       27,841          28,251
                                                                                       3        2,06         19,748      19,069         22,22          22,282
                                                                                       4        2,92         43,214      42,623        15,418          15,538
                                                                                       5        2,69         25,312      24,773        20,064          20,251
            1                                                                         6/7       1,61         22,551      22,421        21,057          21,118
        (data II)
                                                                                   TABLE IV.          THE CALCULATION RESULT OF THE RMSE AND PNSR AT
                                                                                                            CONVOLUTION 4 (DATA I)

                                                                                                                 RMSE                       PNSR
                                                                                    Band                    Hard        Soft          Hard         Soft
                                                                                                          Threshold   Threshold     Threshold    Threshold
  3                                                                                   1         3,27         31,306       30,463       18,274          18,455
        (data II)
                                                                                      2         2,86         32,353       31,691       17,932          18,112
                                                                                      3         2,86           39,3       38,646       15,243          16,389
                                                                                      4         2,72           43,3       42,702       15,401          15,522
                                                                                      5         2,71         48,174       47,818       14,475          14,539
    The RMSE was calculated in the image (the data I and II)
which has been transformed with Haar Wavelet. This RMSE                              6/7        2,08         46,025       45,744       14,871          14,924
values are calculated against several variations of testing which
includes testing of inter-thresholding methods, inter-level                        TABLE V.           THE CALCULATION RESULT OF THE RMSE AND PNSR AT
convolution, and inter-band image. Furthermore, the RMSE is                                                 CONVOLUTION 4 (DATA II)
used as input to the calculation of PNSR to observe the ratio of
                                                                                                                 RMSE                       PNSR
signal strength to noise.                                                           Band
                                                                                              Value         Hard        Soft          Hard         Soft
    Based on the results in Table 1 could be known that                                                   Threshold   Threshold     Threshold    Threshold
visually processes of Haar wavelet denoising did not show the                         1         2,93         31,988         31,1       18,031          18,276
significant results, because the cloud noise in each band is
                                                                                      2         2,57         33,509       32,773       17,628           17,82
represented differently. Therefore, an analysis on the basis of
testing results on PNSR and RMSE are performed.                                       3         2,57         40,198       39,393       16,047          16,222

   The comparison results of RMSE and PNSR on bands 1 to                              4         2,45         43,854       43,025       15,291          15,456
7 with a convolution of 8, 4, and 2 are shown in Table 2 to                           5         2,45         49,071       48,754       14,314          14,371
Table 7. The RMSE and PNSR are obtained can be used to find
out the best band on Landsat satellite imagery for the cloud                         6/7        1,89         46,746       46,469       14,736          14,788
denoising process.
                                                                                   TABLE VI.          THE CALCULATION RESULT OF THE RMSE AND PNSR AT
                                                                                                            CONVOLUTION 2 (DATA I)
                         CONVOLUTION 8 (DATA I)                                                                  RMSE                       PNSR
                                                                                    Band                    Hard        Soft          Hard         Soft
                                RMSE                      PNSR                                Value
         Thresh                                                                                           Threshold   Threshold     Threshold    Threshold
 Band                   Hard         Soft         Hard         Soft
         Value                                                                        1         2,89          7,647        7,362       30,461          30,791
                      Threshold    Threshold    Threshold    Threshold
   1        3,34       30,128          29,633    18,551          18,695               2         2,4          10,745       10,262       27,507          27,906

   2        2,93        30,98          30,356    18,309          18,486               3         2,01         20,123       20,141       22,057          22,049

   3        2,93       38,246          37,681    16,479          16,608               4         2,86         43,812       43,018       15,299          15,458

   4        2,78       42,456          41,998    15,572          15,666               5         2,62         26,025       25,486       19,823          20,005

   5        2,77        46,93          46,548    14,702          14,773              6/7        1,57         22,894       22,873       20,936          20,944

  6/7       2,12       44,859          44,569    15,094          15,15

                                                                                                                ISSN 1947-5500
                                                                         (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                         Vol. 10, No. 1, January 2012
                          CONVOLUTION 2 (DATA II)

                                   RMSE                      PNSR
          Thresh                                                                      In this paper, Discrete Haar Wavelet methods is applied by
 Band                     Hard          Soft         Hard         Soft
                        Threshold     Threshold    Threshold    Threshold         utilize thresholding method to the data testing (Landsat satellite
   1          2,59        7,927           7,835     30,148          30,25
                                                                                  image with size 256x256 pixels) to reduce the noise contained
                                                                                  in image. The testing result shows that the lowest RMSE value
   2          2,15        11,139          10,667    27,194          27,57         is detected on band 1 (29.633) and highest value is on the band
   3          1,8         30,564          20,864    21,869          21,75         5 (49.071). As well as the highest PNSR value observe on the
                                                                                  band I (18.695 dB) and lowest value is on band 5 (14.314 dB).
   4          2,56        44,428          43,333    15,178          15,394        It can be concluded that the best band to perform denoising
   5          2,35        26,787          26,279    19,572          19,739        clouds with Haar Discrete Wavelet found on the band I, and
                                                                                  worst band found on the band 5.
  6/7         1,41        23,313          23,478    20,779          20,178
                                                                                      For further study, is proposed to test the result referable
                                                                                  reinforced with a system of classification on Landsat satellite
    Limitations of different threshold values applied to each                     imagery.
image because the distribution of each image pixels values is
different. This research calculates the threshold based on the
characteristics of image to obtain the best threshold value.
    From Table 2, Table 4 and Table 6 can be seen that the
band 1 has the smallest RMSE values both in hard thresholding
and soft thresholding method (both in the convolution 8, 4, and                   [1]   A. Abd-Elrahman and M. Elhabiby, “Wavelet Enhancement of Cloud-
2). The lowest RMSE values observed in the convolution 8                                Related Shadow Areas in Single Landsat Satellite Imagery”, Beijing:
                                                                                        The International Archives of the Photogrammetry, Remote Sensing, and
with soft thresholding, which is about 29.633 (Data I) and                              Spatial Information Science, Vol. XXXVII part B7, p.1247-1252, 2008.
7.041 (data II). Since the highest RMSE value is detected on                      [2]   H. Choi dan R. Bindschadler, “Cloud Detection in Landsat Imagery of
band 5 (using hard thresholding with convolution 2) that is                             Ice Sheets Using Shadow Matching Technique and Automatic
about 49.071 (Data I) and 26.787 (Data II). The quite far                               Normalized difference Snow Index Threshold Value Decision”, Remote
differences of RMSE value is caused by variations in image                              Sensing of Environment, Vol. 91. p.237-242, 2004.
value. Data I is an image with a lot of noise distribution, while                 [3]   J. Torres and S.O. Infante, “Wavelet Analysis for The Elimination of
the data II has less noise in the form of clouds. Base on RMSE                          Striping Noise In Satellite Images”, Society of Photo-Optical
                                                                                        Instrumentation Engineers, DOI: 10.1117/1.1383996, 2001.
value can be seen that band 2 has the lowest error values and
                                                                                  [4]   M. Beaulieu, M., S. Faucher, and L. Gagnon, « Multi-Spectral Image
band 5 has the highest error value.                                                     Resolution Refinement Using Stationary Wavelet Transform”,
    The highest value of PNSR is observed on the band I that is                         International Geoscience Remote Sensing Symposium, Vol. 6, pp. 4032–
                                                                                        4034, 2003.
around 18.695 dB (data I) and 31.178 dB (data II), while the
                                                                                  [5]   X.H. Wang, Robert S.H. Istepanian, and Y.H. Song, “Microarray Image
lowest value is observed in the band 5 with the value is 14.314                         Enhancement By Denoising Using Stationary Wavelet Transform”,
dB (data I) and 19.572 dB (data II). It means that the ratio of                         IEEE Transactions on Nanobioscience, Vol. 2, No.4, 2003.
the image signal to noise at a band I higher than the band 5.                     [6]   D. F. Alfatwa, “Watermarking pada Citra Digital Menggunakan Discrete
The Signal strength value at Data II tends to be higher than the                        Wavelet Transform”, Informatic Study Program, Technoly Institute of
data I, because the noise in the form of clouds fewer than on                           Bandung, 2005.
the Data I. It denoted that the highest probability to perform                    [7]   R. B. Edy Wibowo, “Scattering Problem for A System of Non Linear
denoising of cloud can be done on the band 1. On the contrary                           Klein-Gordon Equations Related to Dirac-Klein-Gordon Equations”, An
                                                                                        International Multidisciplinary Journal, Vol. 71, No. 3-4, 2009.
the lowest probability is on band 5. These results are quite
relevant to the characteristic of a band I with a wavelength of                   [8]   Gonzales, Rafael C dan Woods, Richard E. 2005. Digital Image
                                                                                        Processing, 2nd Edition. New Jersey: Prentice Hall
0.45 to 0.52 µm which serves to increase penetration on water
body and humidity.

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