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Additional figures, numerical and programming tools as well as exercises for this book may be found at (External Link) .

Preface to the sparse edition

I can not help but find striking resemblances between scientific communities and schoolsof fish. We interact in conferences and through articles, we move together while a globaltrajectory emerges from individual contributions. Some of us like to be at the center of the school,others prefer to wander around, and few swim in multiple directions in front.To avoid dying by starvation in a progressively narrower and specialized domain,a scientific community needs to move on. Computational harmonic analysis is still well alivebecause it went beyond wavelets. Writing such a book is about decoding the trajectory of the school, and gathering the pearls that havebeen uncovered on the way. Wavelets are not any more the central topic, despite the original title.It is just an important tool, as the Fourier transform is. Sparse representation and processing are now at the core.

In the 80's, many researchers were focused on building time-frequency decompositions, trying to avoidthe uncertainty barrier, and hoping to discover the ultimate representation.Along the way came the construction of wavelet orthogonal bases, which opened new perspectives through collaborations with physicistsand mathematicians. Designing orthogonal bases with Xlets became a popular sport, withcompression and noise reduction applications. Connections with approximations and sparsity also became more apparent.The search for sparsity has taken over, leading to new grounds, where orthonormal bases are replaced by redundant dictionariesof waveforms. Geometry is now also becoming more apparent through sparse approximation supports in dictionaries.

During these last 7 years, I also encountered the industrial world. With a lot of naiveness, some bandlets and moremathematics, we created a start-up with Christophe Bernard, Jérome Kalifa and Erwan Le Pennec.It took us some time to learn that in 3 months good engineering should producerobust algorithms that operate in real time, as opposed to the 3 years we wereused to have for writing new ideas with promissing perspectives. Yet, we survived because mathematics isa major source of industrial innovations for signal processing. Semi-conductor technology offers amazingcomputational power and flexibility. However, ad-hoc algorithms often do not scale easily andmathematics accelerates the trial and error development process. Sparsitydecreases computations, memory and data communications. Although it brings beauty,mathematical understanding is not a luxury. It is required by increasinglysophisticated information processing devices.

New additions

Putting sparsity at the center of the book implied rewriting many parts and adding sections. Chapter 12 andChapter 13 are new. They introduce sparse representations in redundant dictionaries, and inverseproblems, super-resolution and compressive sensing. Here is a small catalogue of new elements in this third edition.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
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
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Berger describes sociologists as concerned with
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Source:  OpenStax, A wavelet tour of signal processing, the sparse way. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10711/1.3
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