in my project i am using discrete haar wavelet transform decomposition on image. in that LL,LH,HL,HH subband represents what? and frequency range of each is what?and uses

in my project i am using discrete haar wavelet transform decomposition on image. in that LL,LH,HL,HH subband represents wat? and frequency range of each is what?and uses

Answer 1

[Wayne King]

In the 2-D DWT, the filters are "essentially" halfband filters about the quadrature frequency of pi/2 radians/sample, or 1/4 cycles/sample.

So LL is a separable filtering from [-pi/2 pi/2] in the X-direction and [-pi/2 pi/2] in the Y-direction

LH is a separable filtering from [-pi/2 pi/2] in the X-direction and [-pi -pi/2, pi/2 pi] in the Y-direction

HL is a separable filtering from [-pi -pi/2, pi/2 pi] in the X-direction, and from -pi/2 pi/2] in the Y-direction

HH is a separable filtering from [-pi -pi/2, pi/2 pi] in both X and Y.

Keep in mind that the halfband approximation is much better with longer scaling and wavelet filters -- the Haar is such a short filter that the frequency localization is actually not very good.