CONTINUOUS WAVELET TRANSFORM: Introduction, C-T wavelets,
Definition of CWT, The CWT as a correlation. Constant Q-Factor Filtering
Interpolation and time frequency resolution, the CWT as an operator, inverse
CWT.
UNIT – II
INTRODUCTION TO DISCRETE WAVELET TRANSFORM AND
ORTHOGONAL WAVELET DECOMPOSITION: Introduction.
Approximation of vectors in nested linear vector spaces, (i) example of
approximating vectors in nested subspaces of a finite dimensional liner vector
space, (ii) Example of approximating vectors in nested subspaces of an
infinite dimensional linear vector space. Example MRA. (i) Bases for the
approximations subspaces and Harr scaling function, (ii) Bases for detail
subspaces and Haar wavelet.
UNIT – III
MRA, ORTHO NORMAL WAVELETS AND THEIR RELATIONSHIP
TO FILTER BANKS: Introduction, Formal definition of an MRA.
Construction of a general orthonormal MRA, (i) scaling function and
subspaces, (ii) Implication of dilation equation and orthogonality, a wavelet
basis for MRA. (i) Two scale relations for (t), (ii) Basis for the detail
subspace (iii) Direct sum decomposition, Digital filtering interpolation (i)
Decomposition filters, (ii) reconstruction, the signal.
UNIT – IV
EXAMPLES OF WAVELETS: Examples of orthogonal basis generating
wavelets, (i) Daubechies D4 scaling function and wavelet. (ii) band limited
wavelets, Interpreting orthonormal MRAs for Discrete time MRA, (iii) Basis
functions for DTWT.
PART – B
UNIT – V
ALTERNATIVE WAVELET REPRESENTATIONS: Introduction, Biorthogonal
wavelet bases, Filtering relationship for bi-orthogonal filters,
Examples of bi-orthogonal scaling functions and wavelets. 2-D wavelets.
UNIT – VI
Non - separable multidimensional wavelets, wavelet packets. Wavelets
Transform and Data Compression: Introduction, transform coding, DTWT
for image compression (i) Image compression using DTWT and run-length
encoding.
UNIT – VII
(i) Embedded tree image coding (ii) compression with JPEG audio
compression (iii) Audio masking, (iv) Wavelet based audio coding.
UNIT – VIII
CONSTRUCTION OF SIMPLE WAVELETS: Construction of simple
wavelets like Harr and DB1. Other Applications of Wavelet Transforms:
Introduction, wavelet de-noising, speckle removal, edge detection and object
isolation, Image fusions, Object detection by wavelet transforms of
projections.
REFERENCE
TEXT BOOKS:
1. Wavelet transforms- Introduction to theory and applications,
Raghuveer M.Rao and Ajit S. Bapardikar, Person Education, 2000.
Reference Books
1. Wavelet transforms, Prasad and Iyengar, Wiley estern, 2001.
2. Wave-let and filter banks, Gilbert Strang and Nguyen Wellesley
Cambridge press, 1996