Course

Unit 1

Review of Mathematical Preliminaries, signals and systems course: Review of matrices – vector spaces and linear algebra – Linearly independent – Vector norms – Orthogonality – Eigen values – Eigen vectors – Covariance of matrices – Vector/ function space – Basis function – Orthogonal basis by sampling sine and cosine functions – Singular value decomposition. Significance of time-frequency domains – convolution – Fourier series – Fourier transforms – Review of Fourier theory and properties of fourier transform – DFT-FFT.

Unit 2

Introduction to image processing and wavelet transform: The origins of digital image processing – Examples of fields that use digital image processing – Image digitization and sampling – Image sensing and acquisition – Image sampling and quantization – Image enhancement – Image compression. Continuous wavelet transform (CWT) – Discrete wavelet transform – Haar scaling function nested spaces – Signal decomposition and signal reconstruction using (DWT).

Unit 3

1. K. P. Soman and R. Ramanathan, “Digital signal and Image Processing – The sparse way”, Elsevier India. 2012.

1. K. P. Soman, K. I. Ramachandran, “Insight into Wavelets: From Theory to Practice”, PHI, 2004.
2. Rafael C. Gonzalez and Richard E. Woods, “Digital Image Processing”, Third Edition, Pearson Education India, 2009.
3. Yonina C. Eldar, Gitta Kutyniok, “Compressed Sensing: Theory and Applications”, Cambridge university press, 2012.