<< Chapter < Page Chapter >> Page >
The Conclusion module of the Sparse Signal Recovery in the Presence of Noise collection.

Conclusion

With priming , the regression line correlating number of samples and standard deviation is roughly (sd^2)/6.5 + 1, which amounts to O(N^2) complexity. However, although this may seem slow, our method permits perfect recovery of complicated (albeit sparse) signals with arbitrary levels of AWGN . Thus, for reasonable data set sizes and values of standard deviation, the algorithm functions quite nicely for accurate signal reconstruction. Although if given infinite samples and time, it can recover any signal that is relatively sparse given infinite time.

Without priming the noise, and taking 50 samples, we can achieve O(1) complexity – extremely desirable, but the recovery percentage falls off rapidly with increase in noise standard deviation starting at standard deviation values around 3.5. Thus, this version of the algorithm could be desirable in non-critical applications where the strength of the noise is known to be low relative to that of the signal. We certainly would not recommend using the non-primed algorithm in data sensitive digital applications.

Further avenues of inquiry

Colored noise

It would be interesting to extend the algorithm to accept different types of noise – pink, brown, purple, etc. Logically the exact same algorithm would work on these, but it would be nice to verify this experimentally.

Physical prototype

A physical prototype of this system would allow a far better testing of the theory than simple simulation. Unfortunately, due to the cost of even moderate quality receivers and FPGAs, this was not feasible.

Dynamic noise

One major benefit of a noise resistant system is ECCM, Electronic Counter Countermeasures (counter-jamming). It would be interesting to test whether a system using the described algorithm could resist noise from a transmitter moving towards the system (without simply taking a conservative estimate of worst-case noise during the signal reconstruction period).

Dynamic priming

A useful addition to this algorithm, would be to be able to pick the optimal bound for priming to minimize the number of samples rather than simply choosing the best of two options.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
Berger describes sociologists as concerned with
Mueller Reply
what is hormones?
Wellington
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Sparse signal recovery in the presence of noise. OpenStax CNX. Dec 14, 2009 Download for free at http://cnx.org/content/col11144/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Sparse signal recovery in the presence of noise' conversation and receive update notifications?

Ask