(IJCSIS) International Journal of Computer Science and Information Security,Vol. 10, No. 1, January 2012
threshold is classified as signal. In soft thresholding, thewavelet coefficients with a value below the specified thresholdare removed and the wavelet coefficients above the specifiedthreshold are reduced by the threshold value. Thus, this methodreduces the range of wavelet coefficients and signal leveling.Soft threshold was chosen because this procedure does notcause non-continuants at x = ±
. The equation for the softthreshold is shown in (2).
x xthresh x xsign
(2)For the determination of threshold values is used equationas in (3).
(3)Where:t = threshold value that is calculated= the variance of datan = number of dataThe equation of variance is shown in (4).
n x x
(4)The last process is the Inverse Haar Wavelet Transform(IHWT) which is the process of passing the image through theinverse filter matrix transformations. This process is contrary tothe decomposition process.IV.
METHODFor testing the result is used Root Mean Square Error(RMSE) and Peak-to-Signal Noise Ratio (PNSR).
Root Mean Square Error (RMSE)
RMSE is one of the ways to measure the amount of thedifference between the estimated values with actual values bymeasuring the average of error. RMSE is calculated bycomparing the number of errors between the denoising imageand the original image. The lower the RMSE value the smallerthe error calculation has been done. RMSE of digital imagewith size NxM could be calculated using equation as shown in(5).
N jiF ji f
(5)Where:f(i,j) is pixel value in original imageF(i,j) is the pixel value on reconstruction imageN
is an image size (in pixels)
Peak-to-Signal Noise Ratio (PNSR)
PSNR is the comparison between the maximum possiblesignal strength of a digital signal with the power of noise thataffects on the signal (Alfatwa, 2005). PSNR is defined throughthe signal-to-noise ratio (SNR) to measure the level of signalquality. Signal quality is directly proportional to the value of SNR. The larger of the SNR value, the better the quality of thegenerated signal. PSNR values usually range between 20 and40 dB (Alfatwa, 2005). PSNR values can be calculated usingequation as shown in (6). Value of 255 represents the upperlimit value of image pixels.
DATAImage that is used in the testing process is Landsat TMsatellite image with each channel has a different sensitivity tothe wavelength. Landsat TM satellite orbital period for takingpictures of the earth's surface is generally performed at least 6months. Satellite imagery from two period of taken picture canbe used as a reference on the interpretation process. Forexample, this study used two images with the same object (theisland of Madura) taken in June 2004 and February 2005. Inthe image taken on 2005 exists cloud covering the particularobject and the image taken on 2004 (with the same object) isused as reference.Preparation of satellite imagery should be done to obtainthe image that is suited to analysis. The original image iscropped to the size of 256 x 256 pixels and converted into
extention format. In addition, the original image with 7 bands isseparated per-band for used in applications. Details of the dataused are as follows:1)
Landsat image of Madura island, dated June 25, 2004and dated February 4, 2005
Landsat image of Java island, dated June 25, 2004 anddated February 4, 2005Of the two sources of image data was made 2 pieces of testing data with each of the data contained six band image data(bands 1 to 6 / 7) with each size is 256 x 256 pixels.Data I: latitude 7:7:45.66 S and longitude 113:3:12. 43 EData II: latitude 7:39:41.99 S and longitude 112:56:41.87 EVI.
DISCUSSIONSome examples of images resulted from denoising processare visually displayed in
. The first image shows theresult of denoising on data I (band 1) with convolution 2 (hardthresholding), the second on data II (band 1) with convolution8 (soft thresholding), and the third on data II (band 3) withconvolution 8 (hard thresholding).