Anirban Sengupta - IP Core Protection and Hardware-Assisted Security for Consumer Electronics

This appendix describes the derivation process of Haar wavelet transformation (HWT) CODEC data flow graph using SenguptaRoy HAAR Computation Reduction Functions

HAAR WAVELET TRANSFORMATIONLOSSY CODEC

Equation () shows a generic 512 512 input image in the form of a matrix (A). The subscript and superscript of each element indicate the row and the column numbers of the elements, respectively. For example, the pixel intensity of the third row and 512th column of matrix A is represented by element m3512.

SenguptaRoy HAAR level 1 forward transformation reduction functions

where N is the dimension of the square input image; n is the variable ranging from 1 to N/2, increases in every row; i is the variable ranging from 1 to N/2, increases in every row; p is the variable ranging from 1 to N, increases in every column; j is the variable ranging from N/2 to 1, decreases as i increases. Equation (), where the calculation of pixel intensity is performed based on the aforementioned equations.

Second phase of transformation

where X = WA

SenguptaRoy HAAR level 2 forward transformation reduction functions

where N is the dimension of the square level 1 transformed image; n is the variable ranging from 1 to N, increases in every row; i is the variable ranging from 1 to N/2, increases in every row; p is the odd variable ranging from 1 to N, increases in every column; q is the even variable ranging from 2 to N, increases in every column. The first and second parts of Equation () where the calculation of pixel intensity is performed based on the aforementioned equations.

SenguptaRoy HAAR forward transformation reduction functions

To generate the compressed image matrix B, Equation () is used for calculating the intensity of pixels corresponding to both row and column index greater than N/2 to N.

DFG of HWT-based image compression and scheduled DFG based on four addersubtractor units and four multipliers

where B are the compressed image pixels after applying threshold based on the aforementioned function and T is the hard threshold value.

Image reconstruction

SenguptaRoy HAAR level 1 decompression reduction functions

where N is the dimension of the square-compressed image matrix; z is the variable ranging from 1 to N, increases in every column; x is the variable ranging from 1 to N/2, increases in every alternate row. Equation () where calculation of each pixel is performed based on the aforementioned equations.