IMAGE COMPRESSION ON SCANNING TECHNIQUES: METHODOLOGY (2)

The bands are also referred to as LL, LH, HL and HH respectively, where the first letter represents whether it is low-pass (L) or high-pass (H) filtered along the columns (vertical direction) and the second letter represents whether the low-pass or high-pass filtering is applied along the rows (horizontal direction). If the LL sub-band is iteratively decomposed for analysis, the resulting sub-band partitioning is called the dyadic partitioning.

The algorithm is Calculate a wavelet transforms and orders the coefficients by increasing frequency. This will result in an array containing the image average plus a set of coefficients of length 1, 2, 4, 8, etc. Calculate the median absolute deviation (mad) on the largest coefficient spectrum. The median is calculated from the absolute value of the coefficients.

The equation for the median absolute deviation is given below:

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where Cn,i may be LHn,i, HLn,i, or HHn,i for i-level of decomposition. The factor 0.6745 in the denominator rescales the numerator so that ixcc! is also a suitable estimator for the standard deviation for Gaussian white noise. For calculating the noise threshold X have used a modified version of the equation is,

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Where, N is the number of pixels in the sub image, i.e., HL, LH or HH.

Fluctuations are also created by computing trends along rows followed by trends along columns. The next level of wavelet transform is applied to the low frequency sub band image LL only. The Gaussian noise will nearly be averaged out in low frequency wavelet coefficients. Therefore, only the wavelet coefficients in the high frequency levels need to be thresholded. Apply a thresholding algorithm to the coefficients. There are two popular versions widely used thresholding techniques, hard thresholding and Soft thresholding. Hard thresholding sets any coefficient less than or equal to the threshold to zero. Soft thresholding sets zero value to the coefficient if it is less than or equal to the threshold, else the threshold is subtracted from any coefficient that is greater than the threshold. This moves the image coefficients toward zero.