When we apply haar discrete wavelet transformation to an image we should get four quadrants LL, LH, HL and HH; where LL represents the blurred low-frequency version of the original image. So when I do it with MATLAB using the dwt2 I get it (please see DWT2.png attached). While when I perform linear algebra transformation using the following formula HIH^T; where H is the transformation matrix, I is the original input image and H^T is the transpose of H, I don't get similar results to the dwt2 (please see Transformation.png attached) method which is about high and low pass filtering instead of matrix multiplication. I don't know what's causing such a difference and can't relate between the two!
Thanks in advance.