Audiovisual Communications Laboratory

Signal Processing and Signal Processing and Communications for Sensor NetworksCommunications for Sensor Networks

Martin Vetterli, EPFL and UC Berkeleyjoint work with T. Ajdler, G. Barrenetxea, H. Dubois-Ferriere, F.Ingelrest, M. Kolundzija,

R. Konsbruck, Y. Lu, O. Roy, T. Schmid, L. Sbaiz, E.Telatar, M.Parlange (EPFL), P.L.Dragotti (Imperial), M.Gastpar (UCBerkeley)

Support: Swiss NSF National Center on Mobile Information and Communication Systemshttp://www.mics.org

Thematic Symposium ICASSP 2009Network-Distributed Signal Processing

Spring 2008 - 2

AcknowledgementsAcknowledgements

• To the organizers!

• Swiss and US NSF, our good friends and sponsors

• The National Competence Center on Research ‘’Mobile Information and Communication Systems’’ (MICS)

• The SwissExperiment, a large scale environmental monitoring effort in the Swiss Alps

• K.Ramchandran and his group at UC Berkeley, for sharing pioneering work on distributed source coding

• Colleagues at EPFL and ETHZ involved in MICS - M.Grossglauser, for making things move - E.Telatar, for wisdom and figures! - J.Bovay, for NCCR matters

Spring 2008 - 3

OutlineOutline

1. IntroductionWireless sensor networksFrom “one to one” to “many to many”, or from Shannon to now!

2. The structure of distributed signals and their samplingSensor networks as sampling devices of the real worldDistributed image processing: The plenoptic functionSpatial sound processing: The plenacoustic functionAcquiring the diffusion equation: trade spatial for temporal super-resolution

3. Distributed source codingSource coding, Slepian-Wolf and Wyner-ZivDistributed R(D) for sounds fields

4. On the interaction of source and channel codingTo separate or not to separate... That is the question!The world is analog, why go digital? Gaussian sensor networks

5. Environmental monitoringEnvironmental monitoring for scientific purposes and sensor tomographySensorScope: Real life environmental monitoringin the Swiss Alps

6. Conclusions

Spring 2008 - 4

From centralized to From centralized to ““selfself--organizedorganized””

• Classic solutions (e.g. GSM, UMTS): characterized by heavy fixed infrastructures

• Evolution of wireless communication equipment: computational power , size , price , ~ transmit power

• 110 Billion US$ for UMTS licenses: is there another way?

Ad-hoc networking solution:- multihop, collaborative- reinvented many times- self-organization cute but tricky ; )

Current practice-> hybrid solution: multihop access to backbone-> Sensor Networks

Spring 2008 - 5

The Change of ParadigmThe Change of Paradigm

Old view: one source, one channel, one receiver (Shannon 1948)

Current view: distributed sources, many sensors/sources, distributed communication medium, many receivers!

Note: still many questions open!

ChannelSource Receiver

sourceschannels

receivers

Spring 2008 - 6

Wireless Sensor Networks as Signal Processing DevicesWireless Sensor Networks as Signal Processing Devices

Signals exist everywhere...they just need to be sensed!– distributed signal acquisition: many cameras, microphones etc– these signals are not independent: more sensors, more correlation– there can be some substantial structure in the data,

due to the physics of the processes involvedComputation is cheap

– local computation– complex algorithms to retrieve data are possible

Communication is everywhere– this is the archetypical multi-terminal challenge– mobile ad hoc networks, dense, self-organized sensor networks are built– the cost of mobile communications is still the main constraint

Cross-disciplinarity– fundamental bounds (what can be sensed?)– algorithms (what is feasible?)– systems (what and how to build?)

Spring 2008 - 7

The The swissswiss version of homeland security :)version of homeland security :)

Distributed sensor network for avalanche monitoring:

Method: drop sensors, self-organized triangulation, monitoring of location/distance changes, download when critical situation

Challenges: extreme low power, high precision, asleep most of the time, when waking up, quick download... and all self-organized!

Legacy technology: build a chalet, see if it stands after 50 years!

Spring 2008 - 8

OutlineOutline

1. Introduction2. The structure of distributed signals and their sampling

Sensor networks as sampling devices of the real world PDEs are the name of the gameTemporal sampling is easy….Spatial sampling without filtering!

Distributed image processing: The plenoptic functionHandle with care: not bandlimited!

Spatial sound processing: The plenacoustic functionNon-separable, but essentially bandlimitedSampling theorem, interpolation, and applications

Acquiring the diffusion equationTrade spatial for temporal super-resolutionApplications

3. Distributed source coding4. On the interaction of source and channel coding5. Environmental monitoring6. Conclusions

Spring 2008 - 9

2. The Structure of Distributed Signals and Sampling2. The Structure of Distributed Signals and Sampling

A sensor network is a distributed sampling device

Physical phenomena– distributed signals are governed by laws of physics– partial differential equation at work: heat and wave equation…– spatio-temporal distribution: evolution over time and space

Sampling– regular/irregular, density– in time: easy– in space: no filtering before sampling– spatial aliasing is key phenomena

Note: here we assume that we are interested by the ‘’true’’ phenomena, decision/control: can be different!

Spring 2008 - 10

2. The Structure of Distributed Signals and Sampling2. The Structure of Distributed Signals and SamplingAnalog signals:

Different dimensions have physical meanings (e.g. space and time).

The analog signals are governed by certain physical law.

pollution plume:diffusion equation

sound field:wave equation

plenoptic field:ray model (far field);

wave equation (near field)

Spring 2008 - 11

2. Sampling versus sampling physics (1/4)2. Sampling versus sampling physics (1/4)

1. Classic sampling

– Key: Spaces V, W, bijection f(t) ↔

fk

2. Spatio-temporal sampling

– Temporal filtering easy– No spatial filtering possible!

x

t

Spring 2008 - 12

2. Sampling versus sampling physics (2/4)2. Sampling versus sampling physics (2/4)

3. Sampling physics

– Space V can be partly parametric (e.g. point source, FRI, sparse)– PDE is given by the physics of the problem– No spatial filtering in ϕ(t,x) but PDE does spatial filtering for us!

Goals– From samples find field

– From samples find sources

Spring 2008 - 13

2. Challenges of sampling physics (3/4)2. Challenges of sampling physics (3/4)

Sampling physical fields given by PDEs and driven by sources

Good news:• PDEs are known, and well understood• PDE often regularize the problem (e.g. spatial smoothing)• Some sources are in subspaces

Challenges:• Inhomogeneous dimensions: t and x are indeed different• Cost of sampling in x much higher than in t• Multidimensional sampling, possible non-separable• Regular sampling in time, regular/irregular in space• Sources are in manifolds• Aliasing and undersampling, especially in space, are a real problem• Some events are not bandlimited, and will never be

Spring 2008 - 14

2. Challenges of sampling physics (4/4)2. Challenges of sampling physics (4/4)

Key physical phenomenas:

The wave equation:

• In far field: ray tracing is a good approximation

The diffusion or heat equation:

Navier-Stokes (turbulence):• When averaged: diffusion or heat equation

Random walks:• When averaged: diffusion or heat equation

Spring 2008 - 15

2. Sampling the real world2. Sampling the real world

We consider 3 ‘’real’’ cases, and follow:– what is the physical phenomena– what can be said on the ‘’discretization” in time and space– is there a sampling theorem– what is the structure of the sampled signal

1. Light fields– wave equation for near field– ray tracing for far field– plenoptic function and its sampling

2. Sound fields– wave equation for sounds– plenacoustic function and its sampling

3. Diffusion fields– heat equation– diffusion equation and sampling

Spring 2008 - 16

2.1 The 2.1 The PlenopticPlenoptic Function [Adelson91]Function [Adelson91]

Multiple camera systems– physical world (e.g. landscape, room)– distributed signal acquisition– possible images: plenoptic function, 7-dim!

Background: – pinhole camera & epipolar geometry– multidimensional sampling

Implications on communications– camera sources are correlated in a particular way– limits on number on ‘’independent’’ cameras– different BW requirements at different locations

Spring 2008 - 17

ExamplesExamples

[Stanford multi-camera array]

3D 3D

2D

4D 5D

[Imperial College multi-camera array]

Spring 2008 - 18

2.1 The 2.1 The PlenopticPlenoptic FunctionFunction

t: camera position, v: image plane position

• Epipolar geometry– points become lines– slope depends on depth of field

• Plenoptic function– a collection of lines (modulo covering/uncovering)– slopes banded by (min, max) depth– Fourier transform...a pie slice... can be sampled!

Spring 2008 - 19

2.1 The 2.1 The PlenopticPlenoptic FunctionFunction

Sampling theorem [H.Shum, T.Chen]

Examples of recent results

1. Bandlimited walls/fcts [DoMMV:04] Plenoptic function actually not BL unless linear wall!

ωt

ωs

ωt

ωs

Spring 2008 - 20

2.1 The 2.1 The PlenopticPlenoptic Function [DoMMV:08]Function [DoMMV:08]

Example:

Spring 2008 - 21

2.2 The 2.2 The PlenacousticPlenacoustic Function [AjdlerSV:06]Function [AjdlerSV:06]

Multiple microphones/loudspeakers– physical world (e.g. free field, room)– distributed signal acquisition of sound with “many” microphones– sound rendering with many loudspeakers (wavefield synthesis)

This is for real!– sound recording– special effects– movie theaters (wavefield synthesis)– MP3 surround etc

Wave equation:– Source: BL in time, sparse in space– PDE: essentially BL in (time,space)

MIT1020 mics

Spring 2008 - 22

PlenacousticPlenacoustic function and its samplingfunction and its sampling

Setup

Questions:– Sample with “few” microphones and hear any location?– Solve the wave equation? In general, it is much simpler to sample the

plenacoustic function– Dual question also of interest for synthesis (moving sources)– Implication on acoustic localization problems– Application for acoustic echo cancellation

Spring 2008 - 23

Examples:Examples:

PAF in free field and in a room for a given point source

• We plot: p(x,t), that is, the spatio-temporal impulse response• The key question for sampling is: , that is, the Fourier transform• A precise characterization of for large and will allow sampling

and reconstruction error analysis

Spring 2008 - 24

PlenacousticPlenacoustic function in Fourier domain (approx.):function in Fourier domain (approx.):

Sampled Version:

Thus: Spatio-temporal soundfield can be reconstructed up to ω0

ω:: temporal frequency

Φ: spatial frequency

Spring 2008 - 25

Computed and Measured Computed and Measured PlenacousticPlenacoustic FunctionsFunctions

• Almost bandlimited!• Measurement includes noise and temperature fluctuations

Spring 2008 - 26

A sampling theorem for the A sampling theorem for the plenacousticplenacoustic functionfunction

Theorem [ASV:06]:• Assume a max temporal frequency• Pick a spatial sampling frequency• Spatio-temporal signal interpolated from samples taken atArgument:• Take a cut through PAF• Use exp. decay away from central triangle to bound aliasing• Improvement using quincunx lattice

Spring 2008 - 27

PlenacousticPlenacoustic function in 2Dfunction in 2D

almost bandlimitedTemporal bandwidth: 22 kHz requires one microphone every 1.55 cm!

Spring 2008 - 28

PlenacousticPlenacoustic function: Applicationfunction: Application

Application to wavefield synthesis [M. Kolundzija:09]:• Sound field reconstruction• Wide space equalization

Spring 2008 - 29

Some generalizations: The EM caseSome generalizations: The EM case

Electromagnetic waves and UWB• Wave equation• 3 to 6 GHz temp. frequency• And a triangle!

Spring 2008 - 30

The EM case and TimeThe EM case and Time--Varying ChannelsVarying Channels

Assume a movement model (AR)• Smooth movement• Acts as a modulator• Broadens PAF

The diffusion-advection process (Fick’s law):

where a,b: wind, s: unknown source

Model for: temperature, chemical plumes, smoke from forest fires, radioactive materials ...

Example: heat diffusion in time and frequency

Spring 2008 - 31

The heat equation and diffusion processesThe heat equation and diffusion processes

Spring 2008 - 32

A sampling theory for diffusion processes [Y.Lu:08A sampling theory for diffusion processes [Y.Lu:08--09]09]

Model: diffusion of unknown instantaneous sources (e.g. sudden release of pollutants)

Goal: sample the field using a sensor network, and estimate and .

Assumptions:is a Poisson process, with average time

is (approximately) bandlimited, with bandwidth

Problem Statement:What is the minimum total sampling density? (At least )

What is the trade-off between spatial and temporal sampling rates?

Spring 2008 - 33

A sampling theory for diffusion processes [Y.Lu:08A sampling theory for diffusion processes [Y.Lu:08--09]09]

Spring 2008 - 34

The heat equation and diffusion processesThe heat equation and diffusion processes

Theorem: Sampling a homogeneous diffusion process with Nyquist density fs :

temporalsamples

spatial density

achievable

unachievable

condition number

We have to place the sensors at the right locations!

Spring 2008 - 35

On sampling and representation of distributed signalsOn sampling and representation of distributed signals

We saw a few examples:– Plenoptic function and light fields– Plenacoustic function and sound fields– Heat equation and diffusion processes

It is a general phenomena– Random walks and the heat equation– Electromagnetic fields and wave equation– Diffusion processes and averages of turbulence

This has implications on:– Sampling: where, how many sensors, how much information is to be sensed– Gap between simple (separate) and joint coding– Spatio-temporal waterpouring

Spring 2008 - 36

OutlineOutline

1. Introduction2. The structure of distributed signals and sampling3. Distributed source coding

IntroductionSource coding, sampling, and Slepian-Wolf Distributed rate-distortion function for acoustic fields

4. On the interaction of source and channel coding5. Environmental monitoring6. Conclusions

Spring 2008 - 37

Correlated source coding and transmissionCorrelated source coding and transmission

Dense sources = correlated sources– physical world (e.g. landscape, room)– degrees of freedom ‘’limited’’– denser sampling: sources are more correlated

Background: – Slepian- Wolf (lossless correlated source coding with binning)– Wyner-Ziv (lossy source coding with side information)

Implications on communications– such results are starting to be used...– many open problems (e.g. general lossy case is still an open problem...)– separation might not be the way... are there limiting results?

Below, specific results:– Distributed rate-distortion for acoustic fields based on plenacoustic

function– Also: Distributed compression: a distributed Karhunen-Loeve transform

Optimal data gathering using Slepian-Wolf

Spring 2008 - 38

SlepianSlepian--Wolf (1973Wolf (1973……))

Given– X, Y i.i.d with p(x,y)

Then: encode separately, decode jointly, without coders communicating

Achievable rate region

– R1 ≥

H(X/Y)– R2 ≥

H(Y/X)

– R1 + R2 ≥

H(X,Y)

• For many sources…. rather complex (binning)• Lossy case: mostly open! • Example of result: SW based data gathering [CristescuBV:03]

R1

R2

H(X)

H(Y)

H(X/Y)

H(Y/X)

X

Y

R

Spring 2008 - 39

Distributed source codingDistributed source coding

Spring 2008 - 40

The The plenacousticplenacoustic function as a model, function as a model, KonsbruckKonsbruck (1/4)(1/4)

Stationary spatio-temporal source on a line, measured by a microphone array

Greens’ function

– Fourier Transform essentially supported on a triangle!

Spring 2008 - 41

The The plenacousticplenacoustic function as a model (2/4)function as a model (2/4)

Quincunx sampling lattice

Spring 2008 - 42

The The plenacousticplenacoustic function as a model (3/4)function as a model (3/4)

Quincunx sampling lattice

Key insight: discrete spatio-temporal process is white!

Spring 2008 - 43

The The plenacousticplenacoustic function as a model (4/4)function as a model (4/4)

Distributed rate-distortion functions for white sound field– Centralized– Quincunx sampling based– Rectangular sampling based

– Thus: the distributed R(D) is determined for this case!– For white source, some loss

Spring 2008 - 44

On distributed source codingOn distributed source coding……

Three cases studied:– Data gathering with Slepian-Wolf (Cristescu et al)– Distributed versions of the KLT (Gastpar, Dragotti et al)– Distributed rate-distortion for acoustic fields (above)

These are difficult problems....– lossy distributed compression partly open– high rate case: Quantization + Slepian-Wolf– low rate case: mostly open

In many case– Strong interaction of “source” and ‘’channel’’– Large gains possible

but we are only seeing the beginning of fully taking advantage of the sources structures and the communication medium...

The leads us to revisit the separation principle!

Spring 2008 - 45

OutlineOutline

1. Introduction2. The structure of distributed signals and sampling3. Distributed source coding4. On the interaction of source and channel coding

To separate or not to separate...The world is analog, why go digital? To code or not to code...Gaussian sensor networks

5. Environmental monitoring6. Conclusions

Spring 2008 - 46

4. On the interaction of source and channel coding4. On the interaction of source and channel coding

Going digital is tightly linked to the separation principle:– in the point to point case, separation allows to use

“bits” as a universal currency

– but this is a miracle! (or a lucky coincidence)There is no reason that in multipoint source-channel transmission

the same currency will hold (M.Gastpar)Multi-source, multi-sink case:

– correlated source coding– uncoded transmission can be optimal– source-channel coding for sensor networks

Spring 2008 - 47

4.1 To separate or not to separate4.1 To separate or not to separate……

In point to point, if R < C, all is well in Shannon land. In multipoint communication, things are trickier (or more interesting)

Famous textbook counter example (e.g. Cover-Thomas)

No intersection, but communication possible!

R1

R2

H(X)

H(Y)

H(X/Y)

H(Y/X)

1/3 1/3

0 1/3

Y

X

log23

log23

Source

C1

C2 Channel

1

1

binary erasure multiaccess

Spring 2008 - 48

Sensor networks and source channel codingSensor networks and source channel coding

[GastparV:03/04]Consider the problem of sensing– one source of analog information but many sensors– reconstruct an estimate at the base station

Model: The CEO problem [Berger et al], Gaussian case

Question: distributed source compression and MIMO transmission oruncoded transmission?

Source

W1

W2

WM

U1

U2

UM

X1

X2

XM

F1

F2

FM

GS SY

Z

Spring 2008 - 49

Example: Gaussian Source, Gaussian NoiseExample: Gaussian Source, Gaussian Noise

Performance (cst or poly. growing power shared among sensors):– with uncoded transmission: – with separation:

Exponential suboptimality!

Condition for optimality: measure matching!

––– Can be generalized to many sources

Spring 2008 - 50

It is the best one can do:It is the best one can do:

Communication between sensors does not help as M grows!Intriguing remark:

– by going to ‘’bits’’, MSE went from 1/M to 1/Log(M)– ‘’bits’’ might not be a good idea for distributed sensing and

communicationsIf not ‘’bits’’, what is information in networks? [Gastpar:02]

Spring 2008 - 51

OutlineOutline

1. Introduction2. The structure of distributed signals and sampling3. Distributed source coding4. On the interaction of source and channel coding5. Environmental monitoring

Monitoring for scientific purposesEnvironmental monitoringThe SensorScope projectThe CommonSense project

6. Conclusions

Spring 2008 - 52

Environmental Monitoring: Technological Paradigm Change Environmental Monitoring: Technological Paradigm Change

Monitoring for scientific purposes– “create” a new instrument for critical data– most current acquisitions are undersampled– verification of theory, simulations

Environmental data– unstable terrain, glaciers– watershed monitoring– pollutant monitoring, forest monitoring

Orders of magnitude of difference– price– size– power

We expect this will have a transformational effect on– what is monitored– how it is monitored– what is understood

100K$

1K$ “each”

Today, one of the primary limitations in environmental research is the lack of simultaneous high-density spatial and temporal observations

Today, one of the primary limitations in environmental research is the lack of simultaneous high-density spatial and temporal observations

Spring 2008 - 53

The The SensorScopeSensorScope Project (2005Project (2005--……))

Team: G. Barrenetxea, H.Dubois-Ferriere,T.Schmid,F.Ingelrest, G.Schaeffer + M. Parlange & EFLUM

http://sensorscope.epfl.ch

What are we trying to accomplish?

SensorScope:distributed sensing instrument relevant datasets with clear documentationall data on-line, real-timeanybody can compute/analyze with

Sensor nodes:many possible platforms inc. low power (Berkeley motes, tinynode, tmote)many types of sensing (e.g. cyclops)

First Step: SensorScope Ia few dozen nodesself-organized network up for 9 monthslarge dataset collectedfun platform and testbed

Spring 2008 - 54

The first network!The first network!

Spring 2008 - 55

SensorScopeSensorScope II [w. II [w. M.ParlangeM.Parlange]]SensorScope II

collaboration with EFLUM (Laboratory of Environmental Fluid Mechanics and Hydrology)10 real-world deployments from build to high mountain environmentshundreds of Megabytes of sensing data publicly available

very interesting theoretical (physics) and practical problems!we need reliable and meaningful data!

Improved networkingpacket combining, routing without routesmore power efficient platforms (tinynodes)

Data analysissignals are far from....Gaussian!

Genepi Rock glacier, 2600 m Genepi Rock glacier, your computer

Spring 2008 - 56

The core of The core of SensorScopeSensorScope: : WeatherStationWeatherStationWeatherStation

Centered around Tinynode (lowest-power sensor node, with medium range)Solar energy subsystem: Energy autonomousSensors are daisy-chained to a single connector: No limit on the type and number of sensorsAutomatic sensor recognition: No configuration requiredLocal storage: SD card (2 GB)GPS & GPRS moduleFast and easy installation on all types of terrain:

Spring 2008 - 57

SensorScopeSensorScope Front EndFront End

Features:Centralized data access and administrationReal-time monitoringData visualization and downloadNetwork health and battery statusOrganize stations into setsSet up alerts for out-of-range conditionsSecurity and account managementUser friendly

Spring 2008 - 58

Deployment at EPFL: ResultsDeployment at EPFL: Results

9h00 12h00

13h00 14h00 15h00

17h00Air temperature distributions of EPFL campus from 9h00 to 17h00 November 29th 2006

Spring 2008 - 59

Network architectureNetwork architecture

Sensor network with ad hoc data gathering protocols (10 to 100’s)Basestation with available wide area communication (e.g. GPRS)Web server with data online

Spring 2008 - 60

NetworkingNetworking

Ad Hoc Networking:We use a custom communication stack:Keep it as simple as possible (robustness)Works by overhearing (minimizes traffic)Written for TinyOS 2.x

Main features:Routing tables are updated dynamically(allows to add/remove stations) Radio duty-cycle < 10%(low energy consumption)Stations are synchronized(all “on” at the same time, consistent time stamps) Shortest path routing with random selection (among the “shortest path high quality link neighbours”)

Spring 2008 - 61

Networking: Random, biased selection of next hopNetworking: Random, biased selection of next hop

Spring 2008 - 62

Power is the basic problem!Power is the basic problem!

Communications is power hungryCareful management of powerPower gathering (e.g. solar panels)Energy efficient protocols for data gathering and GPRS connection

Power usage in a Tinynode(a) Off(b) Listening(c)-(g) various sending power

Spring 2008 - 63

From Theory From Theory to Practice!to Practice!

All the tools are there (in theory):Routing algorithms, data correlation, time synchronization,

But ...Make theory work in practice is hard ...

The Theory … The Practice…

Spring 2008 - 64

Real deployment: Grand Saint BernardReal deployment: Grand Saint Bernard

Topology of download tree

Spring 2008 - 65

Real deployment: Grand Saint BernardReal deployment: Grand Saint Bernard

Networks conditionsDriftPower consumptionCode updatesHardware failures

Time drift as a function of Temperature Packet losses during deployment

Spring 2008 - 66

Application Example: Risk AnalysisApplication Example: Risk Analysis

Real problem: land slides, infrastructure damage etc:

Understanding the changing environment, effects of warming, loss of permafrost etc

Spring 2008 - 67

Application Example: Application Example: GenepiGenepi

Location: Rock glacier above Martini (VS)

Spring 2008 - 68

Spring 2008 - 69

A day in the life of A day in the life of GenepiGenepi!!

Fully autonomous camera, GPRS based,Onboard image processing, Open platform, Linux based

Spring 2008 - 70

Results from Results from GenepiGenepi

Spring 2008 - 71

Application Example: Monitoring the Application Example: Monitoring the PatrouillePatrouille des Glaciersdes Glaciers

Spring 2008 - 72

6. Conclusions6. Conclusions

There are some good questions on the interaction of– physics of the process: space of possible values– sensing: analog/digital– representation & compression: local/global– transmission: separate/joint– decoding & reconstruction: applications

From joint source-channel coding to source-channel communication– This goes back to Shannon’s original question,

but multi-source multi-point communication is hard...On-going basic questions:

– are there some fundamental bounds on certain data sets?– are there practical schemes to approach the bounds?– what is observable and what is not?

Applications:– environmental monitoring has many interesting,

high impact questions– technology amazingly mature– datasets very far from ‘’usual’’ models

Spring 2008 - 73

Thank you for your attention! Questions?Thank you for your attention! Questions?

© New Yorker“Would you like to see the top on Google Earth?”

Spring 2008 - 74

ReferencesReferences

• On sampling– M. Vetterli, P. Marziliano, T. Blu. Sampling signals with finite rate of innovation.

IEEE Tr. on SP, Jun. 2002.– T. Ajdler, L. Sbaiz and M. Vetterli, The plenacoustic function and its

sampling, IEEE Transactions on Signal Processing, Oct. 2006. – T. Blu, P.L. Dragotti, M. Vetterli, P. Marziliano and L. Coulot, Sparse Sampling of

Signal Innovations, IEEE Signal Processing Magazine, Vol. 25, Nr. 2, 2008.– M.N. Do, D.Marchand-Maillet, M. Vetterli, On the Bandwidth of the Plenoptic

Function, IEEE Tr.IP, submitted, 2008.– Y.M. Lu and M. Vetterli, Spatial Super-Resolution of a Diffusion Field by

Temporal Oversampling in Sensor Networks, IEEE ICASSP 2009.• Correlated distributed source coding

– R.Cristescu, B.Beferull and M.Vetterli, Correlated data gathering, Infocom2004.– M. Gastpar, P. L. Dragotti, and M. Vetterli. The distributed Karhunen-Loeve

transform. IEEE Tr. on IT, Dec. 06.– R.Konsbruck, E.Telatar, M.Vetterli, The distributed rate-distortion function of

sounds fields, ICASSP06.

Spring 2008 - 75

ReferencesReferences

• On sensor networks, separation uncoded transmission– M.Gastpar, M.Vetterli, PL Dragotti, Sensing reality and communicating bits: A

dangerous liaison - Is digital communication sufficient for sensor networks? IEEE Signal Processing Mag.,July 2006

– M. Gastpar, B. Rimoldi, M. Vetterli. To code or not to code: lossy source-channel communication revisited, IEEE Tr. on IT, 2003

– M.Gastpar, M..Vetterli, The capacity of large Gaussian relay networks, IEEE Tr on IT, March 2005.

• SensorScope– See http://sensorscope.epfl.ch– G. Barrenetxea, F. Ingelrest, G. Schaefer and M. Vetterli,The Hitchhiker's Guide

to Successful Wireless Sensor Network Deployments.,. ACM SenSys2008. – F. Ingelrest, G. Barrenetxea, G. Schaefer, M. Vetterli, O. Couach and M.

Parlange, SensorScope: Application Specific Sensor Network for Environmental Monitoring, to appear in ACM Transactions on Sensor Networks.