Two-dimensional discrete wavelet transform of image

This two-day exposure to image Multiscale decomposition of some content, the main focus on the EMD (empirical mode decomposition)--bemd (bidimensional empirical mode decomposition), LMD ( Local mean decomposition)--BLMD (bidimensional local mean DECOMPOSITION,BLMD).
Have not been exposed to this field before, and now began to slowly do some accumulation, start with the wavelet transform.
1 Image Multiscale decomposition
Because of the different size of the image object and the adaptability of the human visual system to the object scale, a scale dimension is introduced in the image data, and the image is decomposed at various scales. Intuitively speaking, objective objects show different forms according to their distance from the observer, for example, when people observe the same target object at different distances, when they are farther away, they see the whole contour of the object, and in close observation, they see more details about the object. is the multi-scale decomposition of the image.
At present, there are many different kinds of visual comprehension about the word "scale" in multi-scale decomposition of image, such as the resolution of image as the scale of image decomposition, or the size of image object as the scale of image decomposition, or the parameter of convolution kernel for image convolution as the scale of image decomposition.

2 Image Two-dimensional discrete wavelet transform
The two-dimensional discrete wavelet decomposition and reconstruction process of image is described as follows: first, each line of the image is 1D-DWT, the low-frequency component L and the high-frequency component H in the horizontal direction of the original image are obtained, and then each column of the transformed data is 1D-DWT. Obtains the low frequency component of the original image in the horizontal and vertical direction LL, the horizontal direction of the high frequency LH, the horizontal direction of the high frequency and vertical direction of the low frequency HL and the horizontal and vertical direction of the high frequency component HH. The reconstruction process can be described as: first, the transformation results of each column for the discrete wavelet inverse transformation, and then the transformation of the data from each row of one-dimensional discrete wavelet inverse transformation, you can obtain the reconstructed image. As can be seen from the above process, the image wavelet decomposition is a signal in accordance with the low-frequency and high-frequency separation process, the decomposition process can also be based on the need for the LL component further wavelet decomposition, until the requirements are met.

Note: In order to visually reflect the multi-scale decomposition, the following in MATLAB to do a set of tests, simple code as follows:

Load woman;
% X contains image
% image decomposition scale of 2, using SYM5 wavelet
[c,s] = WAVEDEC2 (x,2, ' sym5 ');
The% decomposition scale is 1 Low frequency component
a1 = Wrcoef2 (' A ', c,s, ' SYM5 ', 1); 
The% decomposition scale is 2 low frequency component
a2 = Wrcoef2 (' A ', c,s, ' SYM5 ', 2);

Percent high frequency component
%hl
hd2 = wrcoef2 (' h ', c,s, ' SYM5 ', 2); 
%LH
vd2 = Wrcoef2 (' V ', c,s, ' SYM5 ', 2); 
%hh
dd2 = Wrcoef2 (' d ', c,s, ' SYM5 ', 2);

M=[A2 hd2;vd2 DD2];
Image (M); ColorMap (map);
Axis off;

%%% continues the decomposition of ll
[c,s] = WAVEDEC2 (a2,2, ' sym5 ');
A22 = Wrcoef2 (' A ', c,s, ' SYM5 ', 2);

Hd22 = Wrcoef2 (' h ', c,s, ' SYM5 ', 2); 
Vd22 = Wrcoef2 (' V ', c,s, ' SYM5 ', 2); 
Dd22 = Wrcoef2 (' d ', c,s, ' SYM5 ', 2);
Figure (2);
N=[a22 hd22;vd22 Dd22];
Image (N); ColorMap (map)
; Axis off;

Experimental results:

ll components continue to decompose

Note: After the image has been decomposed, how to analyze is the key to continue reading.