CU7006 WAVELET TRANSFORMS AND APPLICATIONS

CU7006 WAVELET TRANSFORMS AND APPLICATIONS

UNIT I FUNDAMENTALS 9 Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality   and Orthonormality – Relationship Between Vectors and Signals – Signal Spaces – Concept of Convergence – Hilbert Spaces for Energy Signals- Fourier Theory: Fourier series  expansion, Fourier transform, Short time Fourier transform, Time-frequency analysis.

UNIT II        MULTI RESOLUTION ANALYSIS

Definition of Multi Resolution Analysis (MRA) – Haar Basis – Construction of General Orthonormal MRA – Wavelet Basis for MRA – Continuous Time MRA Interpretation for the DTWT – Discrete Time MRA – Basis Functions for the DTWT – PRQMF Filter Banks.

UNIT III CONTINUOUS WAVELET   TRANSFORMS

Wavelet Transform – Definition and Properties – Concept of Scale and its Relation with Frequency – Continuous Wavelet Transform (CWT) – Scaling Function and Wavelet Functions (Daubechies Coiflet, Mexican Hat, Sinc, Gaussian, Bi Orthogonal)– Tiling of Time – Scale Plane for CWT.

UNIT IV DISCRETE WAVELET TRANSFORMS

Filter Bank   and   Sub   Band   Coding   Principles – Wavelet   Filters – Inverse   DWT Computation by Filter Banks – Basic Properties of Filter Coefficients – Choice of Wavelet Function Coefficients – Derivations of Daubechies Wavelets – Mallat's Algorithm for DWT – Multi Band Wavelet Transforms Lifting Scheme- Wavelet Transform Using Polyphase Matrix Factorization – Geometrical Foundations of Lifting Scheme – Lifting Scheme in Z –Domain. 

UNIT V APPLICATIONS

Wavelet methods for signal processing- Image Compression Techniques: EZW–SPHIT Coding – Image Denoising Techniques: Noise Estimation – Shrinkage Rules – Shrinkage Functions – Edge Detection  and Object Isolation, Image Fusion,   and Object Detection. 

TEXT BOOKS: 

1. Rao R  M  and  A  S  Bopardikar, ―Wavelet Transforms Introduction to theory and Applications, Pearson Education, Asia, 2000. 

2. L.Prasad & S.S.Iyengar, Wavelet Analysis with Applications to Image Processing, CRC Press, 1997.

REFERENCES: 

1. J. C. Goswami and A. K. Chan, “Fundamentals of wavelets: Theory, Algorithms and Applications" WileyInterscience Publication, John Wiley & Sons Inc., 1999. 

2. M. Vetterli, J. Kovacevic, “Wavelets and subband coding" Prentice Hall Inc, 1995. 

3. Stephen G. Mallat, “A wavelet tour of signal processing"  2 nd Edition Academic Press, 2000. 

4. Soman K P and Ramachandran K I, ―Insight into Wavelets From Theory to practice‖, Prentice Hall, 2004.