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The Conclusion module of the Sparse Signal Recovery in the Presence of Noise collection.


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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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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
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