The Matching Pursuit algorithm is also used in dictionary learning.

Matching pursuit is related to the field of compressed sensing and has been extended by researchers in that community.

The Matching pursuit is an example of greedy algorithm applied on signal approximation.

The main problem with Matching Pursuit is the computational complexity of the encoder.

Matching pursuit is a greedy iterative algorithm for approximatively solving the original pseudo-norm problem.

In 1993 Mallat and Zhang proposed a greedy solution that is known from that time as Matching Pursuit.

Matching pursuit is a type of numerical technique which involves finding the "best matching" projections of multidimensional data onto an over-complete dictionary .

Matching pursuit suffers from the drawback that an atom can be picked multiple times which is addressed in orthogonal matching pursuit.

Both Matching Pursuit and Orthogonal Matching Pursuit use the norm.

Matching pursuit has been applied to signal, image and video coding, shape representation and recognition, 3D objects coding, and in interdisciplinary applications like structural health monitoring.

The Matching Pursuit algorithm is used in MP/SOFT, a method of simulating quantum dynamics.

Orthogonal Matching Pursuit is similar to Matching Pursuit, except that an atom once picked, cannot be picked again.

In particular, it is used as a measure of the ability of suboptimal algorithms such as matching pursuit and basis pursuit to correctly identify the true representation of a sparse signal.

In LASSO, instead of projecting the residual on some atom as in Matching Pursuit, the residual is moved by a small step in the direction of the atom iteratively.

The concept of matching pursuit in signal processing is related to statistical projection pursuit, in which "interesting" projections were found; ones that deviate more from a normal distribution are considered to be more interesting.

A popular extension of Matching Pursuit (MP) is its orthogonal version: Orthogonal Matching Pursuit (OMP).

Given a fixed dictionary, matching pursuit will first find the one atom that has the biggest inner product with the signal, then subtract the contribution due to that atom, and repeat the process until the signal is satisfactorily decomposed.

As each projection is found, the data are reduced by removing the component along that projection, and the process is repeated to find new projections; this is the "pursuit" aspect that motivated the technique known as matching pursuit.

Michael Korenberg of Queen's University in 1989 developed the "fast orthogonal search" method of more quickly finding a near-optimal decomposition of spectra or other problems, similar to the technique that later became known as orthogonal matching pursuit.

Matching pursuit works by finding a basis vector in that maximizes the correlation with the residual (initialized to ), and then recomputing the residual and coefficients by projecting the residual on all atoms in the dictionary using existing coefficients.

The frequencies are chosen using a method similar to Barning's, but going further in optimizing the choice of each successive new frequency by picking the frequency that minimizes the residual after least-squares fitting (equivalent to the fitting technique now known as matching pursuit with pre-backfitting).

Other methods, such as fractal compression, matching pursuit and the use of a discrete wavelet transform (DWT) have been the subject of some research, but are typically not used in practical products (except for the use of wavelet coding as still-image coders without motion compensation).

A suboptimal expansion can be found by means of an iterative procedure, such as the matching pursuit algorithm (MP) proposed by Mallat and Zhang [ 7 ] In the first step of MP, the waveform 0 which best matches the signal f ( t ) is chosen.

The starting point of spectral decomposition is to decompose each 1D trace from the time domain into its corresponding 2D representation in the time-frequency domain by means of any method of time-frequency decomposition such as: short-time Fourier transform, continuous wavelet transform, Wigner-Ville distribution, matching pursuit, among many others.