OMP Algorithm

This module contains the Orthogonal Matching Pursuit (OMP) algorithm used for sparse coding.

OMP.py - Orthogonal Matching Pursuit (OMP) algorithm for sparse coding.

This module implements the OMP algorithm, which is widely used in compressed sensing and sparse signal recovery. It provides a method to represent signals as sparse combinations of atoms from a given dictionary.

Example usage:

>>> from OMP import OMP
>>> dictio = np.random.randn(100, 200)  # Random dictionary with 200 atoms
>>> signals = np.random.randn(100, 10)  # 10 random signals
>>> sparse_codes = OMP(dictio, signals, max_coeff=5)

CompSensePack.dictionaries.OMP.OMP(dictio, sig, max_coeff)[source]

Orthogonal Matching Pursuit (OMP) algorithm for sparse coding.

This function implements the OMP algorithm, which is used to find the sparse representation of a signal over a given dictionary.

Parameters

dictionumpy.ndarray: The dictionary to use for sparse coding. It should be a matrix of size (n x K), where n is the signal dimension and K is the number of atoms in the dictionary. The columns of the dictionary must be normalized (i.e., each column should have a unit norm).
signumpy.ndarray: The signals to represent using the dictionary. It should be a matrix of size (n x N), where N is the number of signals, and n is the signal dimension.
max_coeffint: The maximum number of coefficients (non-zero entries) to use for representing each signal.

Returns

snumpy.ndarray: The sparse representation of the signals over the dictionary. It will be a matrix of size (K x N), where K is the number of atoms in the dictionary and N is the number of signals.

Notes

This algorithm iteratively selects atoms from the dictionary that are most correlated with the current residual and updates the residual at each iteration.
The process stops when the norm of the residual is sufficiently small or when the maximum number of coefficients (max_coeff) has been reached.
The dictionary’s columns must be normalized before using this algorithm, as the algorithm relies on the assumption that the atoms are unit-norm.

Example

>>> dictio = np.random.randn(100, 200)  # Random dictionary with 200 atoms
>>> signals = np.random.randn(100, 10)  # 10 random signals
>>> sparse_codes = OMP(dictio, signals, max_coeff=5)