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.
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).
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.