transform of wavelet transform are independent each other so only figuring out the influential range of column direction inverse transform is enough to derive minimum number of segment required for decompressing image lines associated to a specific segment thus the previous level coefficients required for column direction inverse transform for each level are described in the followings the notations of the descriptions are explained as follows x ij ld 1 level 1 2 3 d direction c r i row index j column index the minimum range required for decompressing one segment of the entire image frame for real number based inverse transform of equation 1 and integer number based inverse transform of equation 2 is as follows as described above 8 lines of image frame can be associated with each segment the number of image line associated with a specific segment can be described as follows s refers to the number of segment 8 s 8 s 1 8 s 2 8 s 3 8 s 4 8 s 5 8 s 6 8 s 7 the above notations can be modified as follows for separately assigning even and odd components to inverse transform basic formula 8 s 8 s 1 8 s 2 8 s 2 1 8 s 4 8 s 4 1 8 s 6 8 s 6 1 coefficients for level 1 column direction real number and integer inverse transform are summarized as shown table 2 and table 3 as shown in table 2 and table 3 maximum previous 2 and next 3 coefficients are required for 4s stage coefficients as a center since the number of coefficients corresponding to one segment in level 1 transform is 4 minimum number.