# Highly Nonlinear Approximations for Sparse Signal Representation

# Matlab Files

## Duals:

- BioBack deletes the requested vector j from a given basis taken from a dictionary
- BioDictDel deletes a vector from a basis selected from a given dictionary and appropriately modifies biorthogonal functions, orthonormal functions spanning the same space as the basis, and unselected dictionary atoms subtracted by their components in the selected basis.
- BioDictIns enlarges a basis selected from a given dictionary by one vector
- BioFor enlargers the dual/biorthogonal basis enlarger by one vector
- BioInsert adds an atom to a basis. It also appropriately modifies the corresponding biorthogonal basis and orthonormal basis (obtained by modified Gram-Schmidt)
- DRE Dictionary Redundancy Elimination
- DREOr uses DRE method to produce and orthogonal basis from a dictionary and gives dictionary's indices of the atoms spannig the space
- DREOrp uses Dre method to produce and orthogonal basis from a dictionary
- FrDelete deletes the requested vector from a given frame
- FrInsert adds a vector to a frame. It also appropriately modifies the corresponding dual frame
- FrInsertBlock adds vectors to a basis and gives the duals spanning the same space
- NBioDictIns enlarges a basis selected from a given dictionary by one vector. It modifies the biorthogonal basis for the same space and gives the projection of the remainding atoms onto the orthogonal complementary space
- NBioInsert adds an atom to a basis and modifies the biorthogonal basis for the same space

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