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Thread Subject:
Orthogonal Matching Pursuit

Subject: Orthogonal Matching Pursuit

From: kk KKsingh

Date: 28 Apr, 2010 07:46:07

Message: 1 of 7

Hi !

Basically I am from Engineering side ! Not EP ! I need to read a paper on signal recovery from Orthogonal Matching Pursuit ! I dont have hell idea what is this !

Basis pursuit, Orthogonal Matching pursuit ! In which book i can find all this ! I am from engineering background n we didnt study this much maths

Subject: Orthogonal Matching Pursuit

From: kk KKsingh

Date: 28 Apr, 2010 08:00:22

Message: 2 of 7

A example of representation is the Fourier series expansion where the dictionary is built only from basis functions (the smallest possible complete dictionary). The main disadvantage of Fourier analysis in signal processing is that it extracts only global features of signals and does not adapt to analysed signals f. By taking an extremely redundant dictionary we can look in it for functions that best match a signal f. Finding a representation where most of the coefficients in the sum are close to 0 (sparse representation) is desirable for signal coding and compression.


Ok ! This is what i get from wiki ! May be my question is stupid !

1. Suppose my signal is f
2. After that what !

"kk KKsingh" <akikumar1983@gmail.com> wrote in message <hr8p3v$shq$1@fred.mathworks.com>...
> Hi !
>
> Basically I am from Engineering side ! Not EP ! I need to read a paper on signal recovery from Orthogonal Matching Pursuit ! I dont have hell idea what is this !
>
> Basis pursuit, Orthogonal Matching pursuit ! In which book i can find all this ! I am from engineering background n we didnt study this much maths

Subject: Orthogonal Matching Pursuit

From: Wayne King

Date: 28 Apr, 2010 11:25:08

Message: 3 of 7

"kk KKsingh" <akikumar1983@gmail.com> wrote in message <hr8pum$m88$1@fred.mathworks.com>...
> A example of representation is the Fourier series expansion where the dictionary is built only from basis functions (the smallest possible complete dictionary). The main disadvantage of Fourier analysis in signal processing is that it extracts only global features of signals and does not adapt to analysed signals f. By taking an extremely redundant dictionary we can look in it for functions that best match a signal f. Finding a representation where most of the coefficients in the sum are close to 0 (sparse representation) is desirable for signal coding and compression.
>
>
> Ok ! This is what i get from wiki ! May be my question is stupid !
>
> 1. Suppose my signal is f
> 2. After that what !
>
> "kk KKsingh" <akikumar1983@gmail.com> wrote in message <hr8p3v$shq$1@fred.mathworks.com>...
> > Hi !
> >
> > Basically I am from Engineering side ! Not EP ! I need to read a paper on signal recovery from Orthogonal Matching Pursuit ! I dont have hell idea what is this !
> >
> > Basis pursuit, Orthogonal Matching pursuit ! In which book i can find all this ! I am from engineering background n we didnt study this much maths

Hi, Matching pursuit is one of a number of adaptive techniques for choosing the optimal basis depending on the signal. The person to read in this areas is probably Mallat, S. A Wavelet Tour of Signal Processing. Look for the paper
S. Mallat, Z. Zhang, (1993). ``Matching Pursuits with Time-Frequency Dictionaries,'' IEEE Transactions on Signal Processing, 41(12):3397--3415.

If you have the Wavelet Toolbox, you can implement an adaptive basis approach using besttree. See the help for wpdec and besttree.

You can obtain
http://www-stat.stanford.edu/~wavelab/
which is a free Matlab toolbox that implements matching pursuit. There are multiple flavors of matching pursuit, so I'm not sure which one(s) they implement, but if you're interested.

Hope that helps,
Wayne

Subject: Orthogonal Matching Pursuit

From: kk KKsingh

Date: 28 Apr, 2010 13:41:07

Message: 4 of 7

I am working on the signal reconstruction method ! I am having randomly sampled signal ! So planning to work on it by this method

Thanks for your support

Aki

"Wayne King" <wmkingty@gmail.com> wrote in message <hr95uk$k0g$1@fred.mathworks.com>...
> "kk KKsingh" <akikumar1983@gmail.com> wrote in message <hr8pum$m88$1@fred.mathworks.com>...
> > A example of representation is the Fourier series expansion where the dictionary is built only from basis functions (the smallest possible complete dictionary). The main disadvantage of Fourier analysis in signal processing is that it extracts only global features of signals and does not adapt to analysed signals f. By taking an extremely redundant dictionary we can look in it for functions that best match a signal f. Finding a representation where most of the coefficients in the sum are close to 0 (sparse representation) is desirable for signal coding and compression.
> >
> >
> > Ok ! This is what i get from wiki ! May be my question is stupid !
> >
> > 1. Suppose my signal is f
> > 2. After that what !
> >
> > "kk KKsingh" <akikumar1983@gmail.com> wrote in message <hr8p3v$shq$1@fred.mathworks.com>...
> > > Hi !
> > >
> > > Basically I am from Engineering side ! Not EP ! I need to read a paper on signal recovery from Orthogonal Matching Pursuit ! I dont have hell idea what is this !
> > >
> > > Basis pursuit, Orthogonal Matching pursuit ! In which book i can find all this ! I am from engineering background n we didnt study this much maths
>
> Hi, Matching pursuit is one of a number of adaptive techniques for choosing the optimal basis depending on the signal. The person to read in this areas is probably Mallat, S. A Wavelet Tour of Signal Processing. Look for the paper
> S. Mallat, Z. Zhang, (1993). ``Matching Pursuits with Time-Frequency Dictionaries,'' IEEE Transactions on Signal Processing, 41(12):3397--3415.
>
> If you have the Wavelet Toolbox, you can implement an adaptive basis approach using besttree. See the help for wpdec and besttree.
>
> You can obtain
> http://www-stat.stanford.edu/~wavelab/
> which is a free Matlab toolbox that implements matching pursuit. There are multiple flavors of matching pursuit, so I'm not sure which one(s) they implement, but if you're interested.
>
> Hope that helps,
> Wayne

Subject: Orthogonal Matching Pursuit

From: kk KKsingh

Date: 29 Apr, 2010 04:58:03

Message: 5 of 7

Hi !

I read few things, I have a doubt !

Suppose I have a signal ! Now when I FT it I will get the energy spectrum ! These are also known as atoms ! But when signal as singularities it wont able to construct it because of less Coffecients ! So we need to make a dictionary of atoms ! My ques




"Wayne King" <wmkingty@gmail.com> wrote in message <hr95uk$k0g$1@fred.mathworks.com>...
> "kk KKsingh" <akikumar1983@gmail.com> wrote in message <hr8pum$m88$1@fred.mathworks.com>...
> > A example of representation is the Fourier series expansion where the dictionary is built only from basis functions (the smallest possible complete dictionary). The main disadvantage of Fourier analysis in signal processing is that it extracts only global features of signals and does not adapt to analysed signals f. By taking an extremely redundant dictionary we can look in it for functions that best match a signal f. Finding a representation where most of the coefficients in the sum are close to 0 (sparse representation) is desirable for signal coding and compression.
> >
> >
> > Ok ! This is what i get from wiki ! May be my question is stupid !
> >
> > 1. Suppose my signal is f
> > 2. After that what !
> >
> > "kk KKsingh" <akikumar1983@gmail.com> wrote in message <hr8p3v$shq$1@fred.mathworks.com>...
> > > Hi !
> > >
> > > Basically I am from Engineering side ! Not EP ! I need to read a paper on signal recovery from Orthogonal Matching Pursuit ! I dont have hell idea what is this !
> > >
> > > Basis pursuit, Orthogonal Matching pursuit ! In which book i can find all this ! I am from engineering background n we didnt study this much maths
>
> Hi, Matching pursuit is one of a number of adaptive techniques for choosing the optimal basis depending on the signal. The person to read in this areas is probably Mallat, S. A Wavelet Tour of Signal Processing. Look for the paper
> S. Mallat, Z. Zhang, (1993). ``Matching Pursuits with Time-Frequency Dictionaries,'' IEEE Transactions on Signal Processing, 41(12):3397--3415.
>
> If you have the Wavelet Toolbox, you can implement an adaptive basis approach using besttree. See the help for wpdec and besttree.
>
> You can obtain
> http://www-stat.stanford.edu/~wavelab/
> which is a free Matlab toolbox that implements matching pursuit. There are multiple flavors of matching pursuit, so I'm not sure which one(s) they implement, but if you're interested.
>
> Hope that helps,
> Wayne

Subject: Orthogonal Matching Pursuit

From: kk KKsingh

Date: 29 Apr, 2010 05:00:04

Message: 6 of 7

Hi !

I read few things, I have a doubt !

Suppose I have a signal ! Now when I FT it I will get the energy spectrum ! These are also known as atoms ! But when signal as singularities it wont able to construct it because of less Coffecients ! So we need to make a dictionary of atoms ! My question is How to make this dictionary ! Can any one explain me in lay men term !

Below is wiki language

A example of representation is the Fourier series expansion where the dictionary is built only from basis functions (the smallest possible complete dictionary). The main disadvantage of Fourier analysis in signal processing is that it extracts only global features of signals and does not adapt to analysed signals f. By taking an extremely redundant dictionary we can look in it for functions that best match a signal f. Finding a representation where most of the coefficients in the sum are close to 0 (sparse representation) is desirable for signal coding and compression.

Ok What my doubt is ! if i have randomly sampled signal ! How to proceed !

Thanks for your help

Aki

"Wayne King" <wmkingty@gmail.com> wrote in message <hr95uk$k0g$1@fred.mathworks.com>...
> "kk KKsingh" <akikumar1983@gmail.com> wrote in message <hr8pum$m88$1@fred.mathworks.com>...
> > A example of representation is the Fourier series expansion where the dictionary is built only from basis functions (the smallest possible complete dictionary). The main disadvantage of Fourier analysis in signal processing is that it extracts only global features of signals and does not adapt to analysed signals f. By taking an extremely redundant dictionary we can look in it for functions that best match a signal f. Finding a representation where most of the coefficients in the sum are close to 0 (sparse representation) is desirable for signal coding and compression.
> >
> >
> > Ok ! This is what i get from wiki ! May be my question is stupid !
> >
> > 1. Suppose my signal is f
> > 2. After that what !
> >
> > "kk KKsingh" <akikumar1983@gmail.com> wrote in message <hr8p3v$shq$1@fred.mathworks.com>...
> > > Hi !
> > >
> > > Basically I am from Engineering side ! Not EP ! I need to read a paper on signal recovery from Orthogonal Matching Pursuit ! I dont have hell idea what is this !
> > >
> > > Basis pursuit, Orthogonal Matching pursuit ! In which book i can find all this ! I am from engineering background n we didnt study this much maths
>
> Hi, Matching pursuit is one of a number of adaptive techniques for choosing the optimal basis depending on the signal. The person to read in this areas is probably Mallat, S. A Wavelet Tour of Signal Processing. Look for the paper
> S. Mallat, Z. Zhang, (1993). ``Matching Pursuits with Time-Frequency Dictionaries,'' IEEE Transactions on Signal Processing, 41(12):3397--3415.
>
> If you have the Wavelet Toolbox, you can implement an adaptive basis approach using besttree. See the help for wpdec and besttree.
>
> You can obtain
> http://www-stat.stanford.edu/~wavelab/
> which is a free Matlab toolbox that implements matching pursuit. There are multiple flavors of matching pursuit, so I'm not sure which one(s) they implement, but if you're interested.
>
> Hope that helps,
> Wayne

Subject: Orthogonal Matching Pursuit

From: Luca

Date: 11 Aug, 2011 16:08:28

Message: 7 of 7

I have a similar problem as you.
I'm using sparse regression to reconstruct missing data in an image.

There is a specific rule which tell the best solution to adopt in compressive sensing ?

I don't know, may be OMP, or BP, or LASSO.... ???

I think there are so many solutions.... Which one sholud I use?

Thank for any advise

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