I get often different questions from different types of readers and sometimes I cannot think of an answer right away and I find somebody who can or I blog about it. Today I have two questions, if you have an answer, please feel free to answer in the comment or send me a blurb. In the latter case, please also let me know if you want me to use your name:
Angshul Majumdar asked me the following question:
Any specialists out there can help ?
Another reader who shall remain nameless asked the following question:
It looks like an assignment of some sort but I very glad this person asked the question as this was a subject of a conversation I had with some of you including Bob Sturm. The issue at hand is really interesting in that recording is a well known business and plenty of actors in that field have very different offerings in terms of low and high end equipment. So the idea is really, how does a Compressed Sensing method of acquiring an audio signal become disruptive compared to the well established industry ? My take and it is a crazy one, is to see if we can let Nature help. Instead of Imaging with Nature (TM), what about performing Audio with Nature. Any thoughts from any of you on this would be very much welcome. By the way, I am half kidding when I say that we ought to be thinking on how we could perform audio recording on a pottery which we all know is a myth.
In a different area, yesterday, I mentioned a Step-Frequency Radar with Compressive Sampling (SFR-CS) concept out of the Drexel. As an anonymous reader pointed out, the claim of being the first might not be entirely accurate. From the comment:
That paper is here behind a paywall. I had heard about it only through a talk given at Rice. Thank you anonymous reader !
Angshul Majumdar asked me the following question:
Can you please refer a paper, where it is being derived that the Iterative Soft Thresholding is actually solving the l1 regularized least squares problem?
Any specialists out there can help ?
Another reader who shall remain nameless asked the following question:
I have a problem about compressed sensing. My major project is "compressed sensing of audio signal using multiple sensor". Can you help me about method of compressed sensing audio using multiple sensor ?
It looks like an assignment of some sort but I very glad this person asked the question as this was a subject of a conversation I had with some of you including Bob Sturm. The issue at hand is really interesting in that recording is a well known business and plenty of actors in that field have very different offerings in terms of low and high end equipment. So the idea is really, how does a Compressed Sensing method of acquiring an audio signal become disruptive compared to the well established industry ? My take and it is a crazy one, is to see if we can let Nature help. Instead of Imaging with Nature (TM), what about performing Audio with Nature. Any thoughts from any of you on this would be very much welcome. By the way, I am half kidding when I say that we ought to be thinking on how we could perform audio recording on a pottery which we all know is a myth.
In a different area, yesterday, I mentioned a Step-Frequency Radar with Compressive Sampling (SFR-CS) concept out of the Drexel. As an anonymous reader pointed out, the claim of being the first might not be entirely accurate. From the comment:
The authors say "The application of compressive sampling to narrow-band radar systems was recently investigated in [2], [3] and [4], [5], and [6]. The application of CS on SFR has not been investigated before."
Hadn't Gurbuz, McLellan and Scott done GPR using stepped frequency radar in "A Compressive Sensing Data Acquisition and Imaging Method for Stepped Frequency GPRs," IEEE Transactions in Signal Processing, vol. 57, issue 7, pp. 2640-2650 (2009)
That paper is here behind a paywall. I had heard about it only through a talk given at Rice. Thank you anonymous reader !
3 comments:
For the first question of Angshul Majumdar, maybe this paper is what he want.
"An iterative thresholding algorithm fo linear inverse problems with sparsity constraint" by Ingrid Daubechies, Michel Defrise and Christine De Mol.
Definitely, DDD's paper is the best paper for this IST derivation
Definitely DDD is the first reference and it contains the first convergence proof. I would like to add that "Linear convergence of iterative soft-thresholding"
(Kristian Bredies und Dirk A. Lorenz
Journal of Fourier Analysis and Applications, 14(5-6):813-837, 2008) gives an alternative proof and says a bit about the asymptotic rate.
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