What question did this study set out to answer?

To establish theoretical recovery guarantees and performance bounds for the orthogonal matching pursuit algorithm in sparse signal approximation over redundant dictionaries.

September 28, 2004IEEE Transactions on Information Theory

Greed is Good: Algorithmic Results for Sparse Approximation

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Authors

JTJoel A. TroppCalifornia Institute of Technology

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Implication

Algorithmic analysis demonstrates exact sparse signal recovery via orthogonal matching pursuit across quasi-incoherent dictionaries, indicating greedy algorithms achieve near-optimal approximation.

Key Points

To establish theoretical recovery guarantees and performance bounds for the orthogonal matching pursuit algorithm in sparse signal approximation over redundant dictionaries.
Derived sufficient mathematical conditions under which orthogonal matching pursuit and basis pursuit identify optimal sparse representations of exactly sparse signals.
Introduced the cumulative coherence function to generalize incoherence properties to quasi-incoherent dictionary classes.
Demonstrated that orthogonal matching pursuit and basis pursuit reliably recover the exact representation for every sparse signal across quasi-incoherent dictionaries.
Showed that orthogonal matching pursuit acts as an effective approximation algorithm for nonsparse signals, bounding the approximation error to a small factor of the minimal achievable error.

Cite This Study

Joel A. Tropp (2004) studied this question.

synapsesocial.com/papers/6a00412f2ff633f36577dccf https://doi.org/10.1109/tit.2004.834793

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Implication

Algorithmic analysis demonstrates exact sparse signal recovery via orthogonal matching pursuit across quasi-incoherent dictionaries, indicating greedy algorithms achieve near-optimal approximation.

Greed is Good: Algorithmic Results for Sparse Approximation

Discussion

Member takes

Implication

Key Points

Cite This Study

Greed is Good: Algorithmic Results for Sparse Approximation

Discussion

Member takes

Implication

Key Points

Cite This Study

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