# Highly Nonlinear Approximations for Sparse Signal Representation

# Tutorial

This tutorial is intended to be a pedagogical self-contained introduction to the techniques developed within the EPSRC founded project: `` "Highly nonlinear approximations for sparse signal representation".

- List of Symbols
- Elementary Definitions
- Vector Space
- Subspaces - Direct sum
- Linear operators and linear functionals
- Frames and bases for finite a dimension vector space
- Normed vector space
- Inner product space
- Orthogonality
- The spaces , and

- Signal Representation, Reconstruction, and Projection
- Projectors
- Oblique and Orthogonal Projector
- Construction of Oblique Projectors for signal splitting
- Possible constructions of oblique projector
- The need of nonlinear approaches
- Recursive updating/downdating of oblique projectors
- Updating the oblique projector to
- Downdating the oblique projector to

- Signals discrimination by subspace selection

- Sparse representation by minimization of the
norm like quantity - Handling the ill posed case.

- Adaptive non-uniform B-spline dictionaries

- Application to sparse signal representation

- Sparsity and `something else'

- Bibliography
- About this document ...