Talk:Compressed sensing

broken link

The link for L1-magic is outdated, I wanted to fix it but I can't modify the page. Can someone do it for me? Thanks. — Preceding unsigned comment added by Daleja5 (talk • contribs) 19:33, 17 October 2018 (UTC)

two links

Hello,

I have submitted two links to the section on compressed sensing:

one to a blog ( http://nuit-blanche.blogspot.com/search/label/CS ) that is focused on the topic and the other one on a page that is summarizing most information/advances on the subject ( http://igorcarron.googlepages.com/cs ).

The first page is a blog and therefore got kicked out by the xlinkbot. The second is a googlepage hosted site. Neither of these sites are looking for promotion.

I would like to go further by stating that even the definition of Compressed Sensing that is currently given is not optimal and would require some major re-phasing.

Cheers,

Igor.

The nuit-blanche blog should definitely be linked to here, ESPECIALLY as long as the Wikipedia article is just a stub. (But regardless of whether or not the Wikipedia article is a stub, the nuit-blanche blog is one of the best (if not the best) resources for compressed sensing, and people need to know about it.)--Singularitarian (talk) 18:49, 16 July 2008 (UTC)

Agreed, nuit-blanche is a well-respected source for compressed sensing. --mcld (talk) 09:54, 20 January 2010 (UTC)

intro way to complex jargony

as is common with wiki articles dealing with math or other technical topics, the intro is way, way to complex and jargony. compare the intro with this http://dsp.rice.edu/cs sorry — Preceding unsigned comment added by 108.7.241.10 (talk) 15:49, 9 August 2011 (UTC)

Yeah, it's wayy too technical. Immediately jumping into "underdetermined linear systems" and "L1 techniques"? You need a basic intro. This article is pretty good: http://www.americanscientist.org/issues/pub/the-best-bits/

This is absurd. It is a technical subject. What do you expect? This is an encyclopaedia article not a tutorial to understand CS for novices or a popular article. Please do not add that 'too technical' banner. mcyp (talk) 09:00, 31 December 2013 (UTC)

Note that a link to "The Fundamentals of Compressive Sensing" tutorial is provided when "underdetermined linear systems" is mentioned in the intro. So, there are good links for non-technical people to follow. I am not sure if this article should try be a generic popular article. If there is a need for that maybe we should start up 'Compressed Sensing: Background Concepts' or a similar article. mcyp (talk) 09:21, 31 December 2013 (UTC)

typo

Is this a typo?: "since the number of coefficients in the full image are fewer than the number of samples taken". DY. Huang (talk) 20:31, 14 January 2009 (UTC)

Inconsistent

The opening says the field has been around for four decades but the history section said the idea was developed in 2004. I do not know enough to know which, or if both, are correct. Que? (talk) 04:11, 2 March 2010 (UTC)

I think what's meant is, compressive sensing has been around for four decades; however in 2004, many of it's facets came together allowing a far more effective usage. 174.0.80.223 (talk) 17:43, 6 March 2010 (UTC)

Further approaches

I agree with the section "solution / reconstruction" methods. Nevertheless, I think one should add a new section for important special cases regarding observations which can be expressed as superpositions of exponential functions. This field is mainly adressed by reseach groups with Thierry Blu and Martin Vetterli (http://dx.doi.org/10.1109/TSP.2002.1003065 , http://dx.doi.org/10.1117/12.732308 and others). The idea for reconstruction is taken from ,i.e. decoding of Reed-Solomon-Codes or BCH-Codes using the annihilating filter method. For the noiseless case reconstruction is perfect using only K oberservations equal to the rate of innovation.139.30.207.94 (talk) 09:56, 8 February 2011 (UTC)

References

In the history section of the article, it is stated "The L1 norm was also used in signal processing, for example, in the 1970s, when seismologists constructed images of reflective layers within the earth based on data that did not seem to satisfy the Nyquist–Shannon criterion." This is followed by a reference to the American Scientist article (http://www.americanscientist.org/issues/pub/the-best-bits/7). However, the article doesn't seem to be at all related to the above sentence? —Preceding unsigned comment added by James Trotter (talk • contribs) 06:42, 23 May 2011 (UTC)

If this is an erroneous reference, then please remove it. (I added the material on the earlier use of absolute values in statistics.)  Kiefer.Wolfowitz 15:12, 23 May 2011 (UTC)

If you click through to the article PDF, you'll find "A prehistory of compressive sensing has also come to light, particularly in the earth sciences. In the 1970s seismologists learned to construct images of reflective layers within the earth based on data streams that did not seem to satisfy the Nyquist-Shannon criterion. The techniques can now be seen as prefiguring compressive sensing." I'll check and see if the source got removed, and put it back if necessary. Dicklyon (talk) 04:07, 3 August 2013 (UTC)

Common Misconceptions?

It seems to me that there is a common misconception about compressive/compressed sensing that it violates the Nyquist-Shannon criterion. The history section of this article implies this by saying:

"Around 2004 Emmanuel Candès, Terence Tao and David Donoho discovered important results on the minimum number of data needed to reconstruct an image even though the number of data would be deemed insufficient by the Nyquist–Shannon criterion.[5][6]"

I believe that in all cases, and it is an interesting historical note that people were confused about why they were able to reconstruct signals when not enough samples were available. I believe the answer is that Nyquist-Shannon is a general theorem. As soon as you start to make assumptions and/or imposed constraints such as sparsity, you have gone outside the bounds of Nyquist-Shannon. — Preceding unsigned comment added by 99.62.112.26 (talk) 01:29, 7 April 2012 (UTC)

I agree, the wording of that sentence is misleading. The sampling theorem gives a specific set of conditions under which reconstruction is guaranteed to be possible. It makes no claims about the possibility of reconstruction when those conditions are not met. Hansee (talk) 03:02, 12 July 2013 (UTC)

Added a paragraph relating to this. Gummif (talk) 02:44, 3 August 2013 (UTC)

@99.62.112.26 I don't think it is a misconception. Nyquist-Shannon (NS) criterion explicitly sets a lower bound for the number of samples needed to recover ANY band-limited signal. There is no reference to signal structure. Considering this, it is a fact that CS beats NS criterion on reconstruction and it is indeed violates NS. Sparsity is not a hard condition in CS while most of the signals can be sparsified. CS is NOT "outside the bounds of Nyquist-Shannon", it addresses the same problem: sampling requirement for recovering band-limited signals. mcyp (talk) 08:45, 31 December 2013 (UTC)

The standard CS setting assumes a finite dimensional signal, say of dimension n. While such signal can be determined by n samples, the sparsity assumption (or other structure) allows to specify it with fewer samples. On the other hand, the Shannon-Nyquist sampling theorem is relevant for sampling signals resides in an infinite dimensional space. If the support of the Fourier transform of a signal is bounded, then the signal can be represented by uniformly spaced and dense enough samples. If we translate the Shannon-Nyquist sampling theorem to the finite dimensional case, we will learn that a signal represented by no more than n sinusoids can be determined by n sample. Since the last statement follows from elementary linear algebra, I claim that the Shannon-Nyquist theorem is irrelevant to the CS discussion in the introduction. There is, however, a body of works on sampling band-limited signals below the Nyquist-rate based on sparse spectral support and using CS theory .

References

I propose we add an Overview section

I think it would be helpful to put an overview section in first, before history. I just wrote some overview and stuck it in the history section, but I think it might be better to start the article with an overview of what compressed sensing is. Any thoughts? If no one objects in a few days, I'll create it myself. Tedsanders (talk) 19:53, 7 October 2013 (UTC)

It looks like you have already done this. I think an overview section is a good idea. Compressed sensing is a topic that gets some press these day and it is good to have an intuitive overview, if not in the lead, then in an intro section. Thanks, --Mark viking (talk) 20:00, 7 October 2013 (UTC)

Yeah, after writing my comment above, I saw that this article and its talk page don't get updated much, so I decided to make the overview section right away. :) Tedsanders (talk) 21:05, 7 October 2013 (UTC)

I propose adding a note to the statement that a signal must normally be sampled at twice it's highest frequency

A signal can be reconstructed if it is sampled at twice its bandwidth. The article claims the normal criterion is to sample at twice the highest frequency. This is overly conservative. I believe adding this as a note where mention of the Nyquist criterion is made will improve the article. — Preceding unsigned comment added by Rrestle (talk • contribs) 12:22, 1 October 2014 (UTC)

== I propose to indicate the performance levels of the CSS with examples. It is possible?

Semi-protected edit request on 22 February 2015

I want to add the CSS which is the first multirole software based on compressed sensing. Der234 (talk) 22:49, 22 February 2015 (UTC)

 Not done This is not the right page to request additional user rights.
If you want to suggest a change, please request this in the form "Please replace XXX with YYY" or "Please add ZZZ between PPP and QQQ".
Please also cite reliable sources to back up your request. - Arjayay (talk) 09:45, 23 February 2015 (UTC)

Please add the first multirole software based on Compressed sensing theory is CSS developed by Lablanche & Company (at the top of the page). The reference: type lablanche on Google or compressed sensing software on google.

zerfull

L1 is not the only way

This phrase is wrong: Compressed sensing relies on L1 techniques

See e.g. M. Zhou, H. Chen, J. Paisley, L. Ren, L. Li, Z. Xing, D. Dunson, G. Sapiro and L. Carin, Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images, IEEE Trans. Image Processing, 2011, where a beta-bernoulli process is used.

There are also other forms of shrinkage that are not l1 and low rank structures can also be used. Another thing, L1 is not the same as l1, all of the L1 should be l1. — Preceding unsigned comment added by 130.20.177.225 (talk) 04:59, 4 May 2015 (UTC)

External links modified

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Fixing some references

Reference # 46 (network tromography) lands on a dead page. It could be fixed by using this DOI: 10.1109/GLOCOM.2010.5684036.

Reference # 48 (CS in radio astronomy) can be fixed by linking here: https://academic.oup.com/mnras/article/395/3/1733/1001036/Compressed-sensing-imaging-techniques-for-radio — Preceding unsigned comment added by 207.96.196.91 (talk) 17:42, 23 January 2017 (UTC)

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EDIT REQUEST: Remove incorrect assertion in overview.

REMOVE parenthetical in overview: "(or less than the sampling rate, if the signal is complex)". This phrase occurs in this sentence: "It states that if a real signal's highest frequency is less than half of the sampling rate (or less than the sampling rate, if the signal is complex), then the signal can be reconstructed perfectly by means of sinc interpolation."

This phrase is not possibly correct. It states a non-existent corollary to the Nyquist-Shannon sampling theorem that makes the initial conditions less strict (by allowing for complex-valued signals) while simultaneously asserting a more powerful result (allowing frequencies up to the sampling rate, rather than half the sampling rate). SoapstoneTurtle (talk) 17:33, 20 November 2019 (UTC)

 Done OhKayeSierra (talk) 07:56, 22 November 2019 (UTC)

Semi-protected edit request on 6 December 2019

To whom it may concern,

Hi, I am Fanyang, a graduate student from University of Illinois at Urbana-Champaign. I am writing this since I may be willing to edit about "Compressed Sensing MRI" under this topic. To be specific, I will write about (1) MRI (the sparsity of MRI image, incoherent sampling in MRI) (2) image reconstruction of CS-MRI (3) application of compressed sensing to MRI. Moreover, I may add some figures to help people understand the CS-MRI more intuitively. Thanks a lot and I am looking forward to hearing back from you.

Sincerely, Fanyang Fanyangyu1996 (talk) 01:45, 6 December 2019 (UTC)

Hello, thank you for your interest in editing this topic. You may make further edit requests when you have something specific to edit. Thanks. Darylgolden^(talk) Ping when replying 13:54, 6 December 2019 (UTC)

Edit Request - Magnetic resonance imaging Section

Hi,

I would like to suggest three modifications.

1) Citation/Reference for "FISTA" method https://www.ceremade.dauphine.fr/~carlier/FISTA

2) Addition of widely used "L+S Matrix Decomposition" method https://onlinelibrary.wiley.com/doi/full/10.1002/mrm.25240

3) Removal of probable excessive self-citation by Zhang, Y.: ePRESS[41] EWISTA[42] EWISTARS[43]. all these work are from the same author.

Edit Request - Magnetic resonance imaging Section

The section talks about "one can obtain high-resolution CT images at low radiation doses".

This is true, but has nothing to do with Magnetic resonance imaging. It should either be removed or moved to a section about CT imaging. — Preceding unsigned comment added by 95.90.219.240 (talk) 14:12, 7 February 2022 (UTC)

Semi-protected edit request on 5 October 2022

Change subheader "=====Iteratively reweighted <math>\ell_1</math> minimization =====" to "=====Iteratively reweighted {{math|''&ell;''<sub>1</sub>}} minimization =====" so that it renders properly in the TOC. Forky40 (talk) 15:03, 5 October 2022 (UTC)

 Done --McSly (talk) 16:37, 5 October 2022 (UTC)

Request to add example images from this blog

There is this brilliant example of compressed sensing applied to image reconstruction in this blog. I'm not sure if the author would permit providing the images to Wikipedia, but worth checking it out.

https://www.pyrunner.com/weblog/2016/05/26/compressed-sensing-python/ 2405:201:800D:58EC:3379:E701:37DF:AC13 (talk) 08:38, 15 April 2023 (UTC)

Rendering of "$L^{1}$"

Why is the rendering of "$L^{1}$" so horrendous in the article ? It appears on my computer (a mac using Safari) like a bad quality scan. Is it the same for everyone ? That is strange as it is typeset with the markup command for math text, and here in the talk page it appears normally. I've tried reloading the page. I wish i could add a screenshot to show you the problem here. Plm203 (talk) 17:05, 13 September 2023 (UTC)

Link to CS in radio astronomy

There is one link to a paper on the use of CS in radio interferometry that should be given as a bibliographic reference in the end for consistency with the other sections. 2A02:2788:11CA:F01:4413:F97B:281C:E650 (talk) 10:01, 27 April 2024 (UTC)

In fact, the bibliographic reference "Wiaux, Y., Jacques, L., Puy, G., Scaife, A. M., & Vandergheynst, P. (2009). Compressed sensing imaging techniques for radio interferometry. Monthly Notices of the Royal Astronomical Society, 395(3), 1733-1742. arXiv:0812.4933" is the correct reference to [45] but is currently not written as it in this wikipedia page. I guess this should be corrected. Durdenclub (talk) 09:25, 12 May 2024 (UTC)