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Background

Module by: Genaro Picazo. E-mail the author

Summary: Background for our ELEC 301 Project for Fall 2003. By: Chris Omidiran, Genaro Picazo, Ian Wells, Daniel Wu

Algorithms

The two algorithms that we are concerned with are basis pursuit (BP) and orthogonal matching pursuit (OMP). What these two algorithms have in common is a requirement to use waveforms from a dictionary to represent an image. One advantage of these two algorithms is that they are very flexible in terms of the dictionary used, which in turn allows for faster, sparser compression. It has been previously shown that while OMP is a faster algorithm, BP yields a mroe accurate approximation.

Basis Pursuit

Basis pursuit is an effective algorithm which replace the sparse approximation problem by a linear programming problem. It selects the coefficients that will represent the signal to be those with the minimum L1 coefficients. Essentially what it does is the following: Given a signal X, it takes the inner product of X with each element in the dictionary and at the end takes selects the one that yields the larger result (this will be the element the most closely resembles X). This element is added to previously selected elements, and subtracted from the signal X. It does repeat this process on the residual signal until N elements have been chosen, where N is the number of desired coefficients in the approximate representation of X.

Orthogonal Matching Pursuit

Orthogonal matching pursuit is an iterative greedy algorithm that chooses the dictionary element that best represents the residual part of the signal at each iteration (just like the BP algorithm). It then projects this element onto those elements which have already been selected, which yields a new approximant signal. This differs from the BP algorithm in that redundant information is not repeated.

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

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'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks