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

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.

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.

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

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

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

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

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)

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

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

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

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