# Highly Nonlinear Approximations for Sparse Signal Representation

# Matlab Files

## Wavelet Spline Dictionaries:

- BuildDict helps you to construct a multiresolution-like spline wavelet dictionary or a B-spline dictionary
- ElimBound eliminates redundant boundary wavelets to have a basis for the cut-off spline wavelet dictionary constructed with b=1
- GDictFast generates dictionaries by translating prototype functions
- NumFun states how many functions f(a^j*x-b*k), where k is an integer, have non-trivial intersection with the interval [c,d]
- SPL generates B-splines of order m at scale j with translation parameter k, B(a^j*x-k). Multiple knots for construction boundary functions are considered
- STPoint returns such a translation parameter k that f(a^j*x-b*k) is the first function having non-trivial intersection with the point c
- ScalLevel generates a set of all translated B-splines, B(a^j*x-b*k), having non-trivial intersection with the given interval. It can be also used for construction (Chui) cubic B-spline basis (for b=1 only)
- SplineWavelet generates semi-orthogonal spline wavelet, w(a^j*x-b*k), of order 1,2 or 4 on the given interval
- WavLevel generates a set of all translated spline wavelets, w(a^j*x-b*k), having non-trivial intersection with the given interval. It can be also used for construction (Chui) cubic B-spline wavelet basis (for b=1 only)

All the presented routines are described in detail in our manual (ps,pdf).