Discrete time wavelet transforms (DWT), which produces multi-scale image decomposition. By employing filtering and sub-sampling, a result in the form of the decomposition image (for classical dyadic approach) is produced, very effectively revealing data redundancy in several scales. A coding principle is then applied in order to compress the data. It superior to Fourier and DCT. It has Discrete Wavelet Transform (DWT) provides a multi resolution image representation and has become one of the most important tools in image analysis and coding over the last two decades. Image compression algorithms based on DWT provide high coding efficiency for natural (smooth) images. As dyadic DWT does not adapt to the various space-frequency properties of images, the energy compaction it achieves is generally not optimal. It has been widely applied and developed in image processing and compression.
There exist two ways how to implement the computation of the discrete-time wavelet transform. The first approach uses convolution (filtering) with appropriate boundary handling, the second is a fast lifting approach, a refined system of very short filters which are applied in a way that produces the same result as the first approach, introducing significant computational and memory savings .Lifting scheme is derived from a polyphase matrix representation of the wavelet filters, a representation that is distinguishing between even and odd samples. Using the algorithm of filter factoring, we split the original filter into a series of shorter filters (typically Laurent polynomials of first degree). Those filters are designed as lifting steps; each step one group of coefficients are lifted(altered) with the help of the other one (classical dyadic transform always leads to two groups of coefficients, low-pass and high-pass).
Since images are two-dimensional signals, we have to extend the scheme to 2D space by applying the transform row and column-wise,respectively(taking separability of the transform into account).
As a consequence four subbands arise from one level of the transform – one low-pass subband containing the coarse approximation of the source image called LL subband, and three high-pass subbands that exploit image details across different directions – HL for horizontally for vertical and HH for diagonal details. IN the next level of the transform, we use the LL band for further decomposition and replace it with respective four subbands. This forms the decomposition image.
Advantages:
1. DWT has excellent energy compaction capabilities and hence the coding technique must be well-designed to achieve significant image compression.
2. At low bit rate, DWT avoid the blocking artifacts of DCT.
3. It presents better coding performance.
Syntax:
[cA,cH,cV,cD] = dwt2(X,'wname')
computes the approximation coefficients matrix cA and details coefficients matrices cH, cV, and cD (horizontal, vertical, and diagonal, respectively), obtained by wavelet decomposition of the input matrix X. The 'wname' string contains the wavelet name.
[cA,cH,cV,cD] = dwt2(X,Lo_D,Hi_D)
computes the two-dimensional wavelet decomposition as above, based on wavelet decomposition filters that you specify.
Lo_D is the decomposition low-pass filter.
Hi_D is the decomposition high-pass filter.
Lo_D and Hi_D must be the same length.
Program & Output:
Syntax:
[cA,cH,cV,cD] = dwt2(X,'wname')
computes the approximation coefficients matrix cA and details coefficients matrices cH, cV, and cD (horizontal, vertical, and diagonal, respectively), obtained by wavelet decomposition of the input matrix X. The 'wname' string contains the wavelet name.
[cA,cH,cV,cD] = dwt2(X,Lo_D,Hi_D)
computes the two-dimensional wavelet decomposition as above, based on wavelet decomposition filters that you specify.
Lo_D is the decomposition low-pass filter.
Hi_D is the decomposition high-pass filter.
Lo_D and Hi_D must be the same length.
Program & Output:
clc
[file path]=uigetfile('*.*');
a=imread(file);
figure;imshow(a)
[ca ch cv cd]=dwt2(a,'haar');
figure;imshow([(ca/512),ch;cv,cd])
figure;
subplot(2,2,1);imshow(ca/512);title('Approximation')
subplot(2,2,2);imshow(ch);title('Horizontal')
subplot(2,2,3);imshow(cv);title('Vertical')
subplot(2,2,4);imshow(cd);title('Diagonal')
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Fig: Barbara Original Image
Fig: Separate Subbands
Fig: Combined Subbands
Contact:
Mr. Roshan P. Helonde
Mobile: +91-7276355704
WhatsApp: +91-7276355704
Email: roshanphelonde@rediffmail.com
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