# Highly Nonlinear Approximations for Sparse Signal Representation

# Matlab Files

## Uniform Spline Dictionaries:

- BSpline gives the analytical form of k-th B-spline of order m on l-th subinterval of given partition t
- DictSpline generates dictionary of cardinal B-spline functions of order m
- Differ calculates (s-1)-th divided difference of \max((t-x)^(m-1),0) where s is the number of knots in sequence t (i.e., s=length(t))
- ErrorTest tests orthogonality of a sequence or biorthogonality of two sequences
- Green calculates (x_+)^m = x^m for x>=0 (it is 0 for x<0). This functions is known as truncated powers
- NormDict normalizes a given dictionary
- SplineLevel generates a B-spline dictionary depending on given parameters
- SymSpline gives the analytical form of B-spline of order m with knots in partition t
- TSpline generates B-spline basis of order m corresponding to knot sequence t

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