COURSE SUMMARY
Course Title: 
Sparse Signal and Image Processing
Course Code: 
15ECE332
Year Taught: 
2015
Type: 
Elective
Degree: 
Undergraduate (UG)
School: 
School of Engineering
Campus: 
Bengaluru
Chennai
Coimbatore
Amritapuri

'Sparse Signal and Image Processing' is an elective course offered for the B. Tech. (Bachelor of Technology) in Electronics and Communication Engineering at School of Engineering, Amrita Vishwa Vidyapeetham.

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

Compressed sensing and Sparse Signal Representation: Sparse signals - Single pixel imaging - Compressible signals - over complete dictionaries - Coherence between bases - Compressed sensing and signal reconstruction - Restricted isometry property - Unconstrained and constrained optimization algorithms – Applications of compressed sensing in different fields.

TEXTBOOKS

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

REFERENCES

  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.