Multi-Scale Sampling

Outline

• Introduction• Information technology challenges• Example: light patterns in forest

Greg Pottie

Pottie@icsl.ucla.edu

Example: Light Pattern Sampling

• Photosynthesis begins above some (species-specific) incident light intensity threshold, and eventually saturates– Pattern of light levels thus conveys more useful information than simple

average of intensity

• Do not necessarily need to reconstruct the field

• Selected statistics may be sufficient– E.g. histograms of intensity

levels, characterization of light level dynamics

• Natural scenes are very complicated– Shadows from many levels

Some Early NIMS PAR Measurements

• Large variations over short distances– Pure static network will

require unreasonable density for field reconstruction

• Pure mobile network will give misleading results with respect to rapid dynamics (e.g. branches blowing in wind)

• Some type of hybrid strategy suggested

Adaptive Sampling Strategies

• Over-deploy: focus on scheduling which nodes are on at a given time

• Actuate: work with smaller node densities, but allow nodes to move to respond to environmental dynamics

• Our apps (Terrestrial, Aquatic, Contaminant) are at unprecedented scales and highly dynamic: over-deployment is not an option– Always undersampled with respect to some

phenomenon

– Focus on infrastructure supported mobility

– Passive supports (tethers, buoyancy)

– Small number of moving nodes

• Many approaches/experiments explored in past two years

Speedup using Static and Mobile Nodes

t=1

t=2

t=3

• Static nodes act as triggers• Network of static nodes ‘allocates’ tasks to mobile nodes

Sampling

• Lattice/deterministic pattern• Gradient methods (e.g. Newton, LMS)• Simulated annealing (guided walks)• Multi-scale or multi-dwell• Bisection/quad algorithms (decision

trees with multiple depths)• Random walk

• Sampling strategy depends on physical model, objectives, and available resources

• E.g., finding global max or min of a field depends on smoothness:

Smooth

Rough

• Similar stacks can be constructed for other sampling objectives (e.g., reconstruction, gathering statistics)

Multiscale Approach

• Goal is optimization of the hierarchical system– Not merely optimization of devices or any given

layer

– Models, devices, algorithms require co-design

• Context-driven algorithms– No single algorithm/device is best in all

situations

– Context is the state of the next level in the hierarchy; choose resources to apply when drilling down to next level according to this state

– Probabilistic constraints and algorithms lead to more new optimizations

• Examples: adaptive and multi-scale sampling

Optimization Paradigm

Humans

State Detection

Algorithms for each state

Minimize involvement in routine tasks; employ for difficult cognitive tasks

State of next model in hierarchy determines which algorithmic suite to use

Can have multiple algorithms, possibly hierarchically arranged

Play probability game to minimize costs of higher level reasoning; employ hierarchy of algorithmic approaches

Multi-level Processing

• Goal: construction of tree of (re-usable) algorithms and models relating physical structure of forest canopy to light levels on forest floor, and consequences for plant growth.

• Physical Model:– Fixed elements: trunks, major branches,

topography (deterministic)

– Variable elements: branches, leaves, sun position, clouds (statistical)

• Algorithmic Set:– Search algorithms to create maps of canopy and

ground patterns; complexity and choice will vary spatially

– Higher level reasoning to relate data to science question, determine model parameters (e.g., Bayes, rule-based, formal optimizations)

Physical Models

• Models apply at different levels of abstraction– Abstraction level(s) much match query

• Example: information from sources– Attenuation with distance from source

– Statistical description (e.g., Correlations in time/space/transform domain, source and environmental dynamics)

– Disk model

– Statistical aggregations (e.g., flows on graph representing network)

• Model depends also on sensor data– Different statistics at different spatial scales and

for different sensing modes

– Data set affects number of viable hypotheses

• Feasibility depends on algorithmic availability– Need computationally effective suite

Model Uncertainty in Sensor Networks

• How much information is required to trust a model?

• Approach: information theoretic analysis of benefits of redundancy and auditing in model creation

• Will be backed up by simulations and experiments

In how many locations must a field be sampled (by combination of static and mobile nodes) to determine it is caused by one (or more) point sources?

Data Integrity

Multiple nodes observe source, exchangereputation information, and then interactwith mobile audit node

• How can we trust the data produced by a sensor network?

• Approaches– Redundant deployment

– Mobile auditors

– Hybrid schemes

• Components– Reputation systems

– Statistical analysis of information flows

Multi-scale sampling

• A homogeneous screen is placed to create a reflection Er proportional to incident light Ec.

• Camera captures the reflection on its CCD

• The image pixel intensity is transformed to Er using camera’s characteristic curve.

• Sensors with different modes and spatial resolutions– E.g. NIMS PAR sensor and

camera– PAR measures local incident

intensity– Camera measures relative

reflected intensity

• Provides better spatial and temporal resolution, at cost of requiring careful calibration

• Analogous to remote sensing on local scales

Conclusion

• multi-layered systems provide major opportunities– Overall complexity can be significantly reduced, from both

hardware and software perspective– Re-use of components in a variety of settings

• Multi-layered systems present many research challenges– Fundamental research questions in model construction, data

and model uncertainty, information flows among layers, and large-scale systems design/optimization

– Necessary to pursue mix of lab and field experiments to ensure realism in problems and generality of results