1. Design and Implementation of Lossless DWT/IDWT (Discrete Wavelet Transform & Inverse Discrete Wavelet Transform) for Medical Images

2. Introduction Why Discrete wavelet transform
The wavelet transform has gained widespread acceptance in signal processing and image compression. Because of their inherent multi-resolution nature, wavelet-coding schemes are especially suitable for applications where scalability and tolerable degradation are important
Applications of the project
Medical application
Signal de-noising
Data compression
Image processing
What is an image?
An image (from Latin imago) or picture is an artifact, usually 2-Dimentional, that has a similar appearance to some object or person
What is an image compression?
Image compression is minimizing the size in bytes of data without degrading the quality of the image to an acceptable level.

3. Introduction (cont..) There are two types of compressions 1.Lossless
Digitally identical to the original image. Only achieve a modest amount of compression
2.Lossy
Discards components of the signal that are known to be redundant. Signal is therefore changed from input
Lossless compression involves with compressing data, when decompressed data will be an exact replica of the original data. This is the case when binary data such as executable are compressed.
What is wavelets?
Wavelet transform decomposes a signal into a set of basis functions. These basis functions are called wavelets
What is Discrete wavelet transform?
Discrete wavelet transform (DWT), which transforms a discrete time signal to a discrete wavelet representation.

4. Introduction (cont..) Lossless and Lossy LOSSY LOSSLESS
1.Huffman coding
2.LZW
3.Run length coding
LOSSY
Predictive
Frequency oriented
Hybrid
Importance oriented
DCT
DWT
Transform
Fractal
Mallat
Transversal filter
Codic
Lifiting Scheme

5. Literature Review
Lifting schema of DWT has been recognized as a faster approach
The basic principle is to factorize the poly-phase matrix of a wavelet filter into a sequence of alternating upper and lower triangular matrices and a diagonal matrix .
Figure 2 Image compression levels

6. Literature Review (cont..)
2-D DWT for Image
Figure 3 Image compression and decoded image

7. 2-D (5, 3) DWT – Lossless Transformation
The even and odd coefficient equations for (5, 3) Inverse Integer Wavelet Transform are

8. The 2-D (5, 3) Discrete Wavelet Transform
Figure Computation of Basic (5, 3) DWT Block in which ‘a’ and ‘b’ are
lifting coefficients (a = -1/2 and b = 1)

9. Simulation Results DWT Block
Figure Simulation Result of DWT-1 Block with Both High and Low Pass

10. Figure Simulation Result of DWT-2 Block with Both High and Low Pass Coefficients

11. Figure Simulation Result of DWT-3 Block with Both High and Low Pass Coefficients

12. THANK YOU