a compressive sensing and swarm optimization algorithm for

A compressive sensing and swarm optimization algorithm for 4W1H in the

Intelligent Space

Leon F. Palafox

Hashimoto Laboratory

M2

37-086946

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Outline

• Introduction– Intelligent Space– Compressive Sensing– Swarm Intelligence

• Particle Swarm Optimization

• Motivation• Algorithm Description• Hardware Description• Results• Conclusions• Future Work

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IntroductionIntelligent Space

• Intelligent Space (ISpace) is a space that has ubiquitous distributed sensory intelligence and actuators for manipulating the space and providing useful services.

• It can be regarded as a system that is able to support humans, i.e. users of the space, in various ways.

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IntroductionCompressive Sensing

• In almost all the applications when sampling we must follow Shannon/Nyquist theorem that requires sampling rate at least twice the message signal bandwidth in order to achieve exact recovery.

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PICTUREORTHO-

GONALIZITIONSORTING CODING

Full set of projections is found

K largest coefficients selectedN-K coef. dumped

Only K coefficients are coded

EXAUSTIVE SEARCHEXAUSTIVE SEARCH

PICTURE CODING

K<<N

N samples(ALLmeasurementsare taken)

Straightforward decoding

Straightforward decoding

Signal Reconstruction(1) Underdetermined system M<N (2) Reconstructed signal must have N components(3) L1 norm is used to find sparse representation

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• Compressed sensing is new method to capture and represent compressible signals at the rate well below Nyquist’s rate.

– Employs nonadaptive linear projections (random measurement matrix)

– Preserves the signal structure (length of the sparse vectors is conserved)

– Reconstructs the signal from the projections using optimization process (L1 norm)

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(a) Compressive sensing measurement process with a random Gaussianmeasurement matrix and discrete cosine transform (DCT) matrix . The vector of coefficients s is sparse with K = 4.

Φ (phi, measurement matrix) Ψ (psi, orthonormal basis) Θ (theta, Compressed Sensing reconstruction matrix)

(b) Measurement process


y

= =

Φ Ψ S y Θ S

x

K-sparseN

(a) (b)

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• M measurements, y, random measurements matrix, Φ, and basis Ψ, are used to reconstruct compressible signal x (length) N or equivalently its sparse coefficient vector s.

• Since M<N there are infinitely many solutions. Since Θ(s+r)= Θ(s)=y for any vector r in the null space N(Θ). But we have a restriction that the solution is sparse.

• Signal reconstruction algorithm aims to find signal’s sparse coefficient vector in the (N-M)-dimensional translated null space H=N(Θ)+s. – L1 norm (adding absolute values of all elements) can exactly recover K

sparse signals and closely approximate compressible signals with high probability


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IntroductionSwarm Intelligence

• Is a type of artificial intelligence based on the collective behavior of decentralized, self-organized systems.

• The expression was introduced by Gerardo Beni and Jing Wang in 1989, in the context of cellular robotic systems

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IntroductionParticle Swarm Optimization

• Is a population based stochastic optimization technique developed in 1995, inspired by social behavior of bird flocking or fish schooling.

• PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). – The system is initialized with a population of random solutions

and searches for optima by updating generations.

• It has no evolution operators such as crossover and mutation. – In PSO, the potential solutions, called particles, follow the

current optimum particles.

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IntroductionParticle Swarm Optimization

• Each particle keeps track of its coordinates in the problem space which are associated with the best solution (fitness) it has achieved so far. – Another "best" value that is tracked by the particle swarm optimizer is

the best value, obtained so far by any particle in the neighbors of the particle.

– When a particle takes all the population as its topological neighbors, the best value is a global best.

• The particle swarm optimization concept consists of, at each time step, changing the velocity of (accelerating) each particle toward its best locations (local version of PSO).

• Acceleration is weighted by a random term, with separate random numbers being generated for acceleration toward the best locations.

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Motivation

• There is currently in the ISpace some background on people activity detection.

• The most advance work in this topic is called 4W1H

• Who• When• What• Where• How

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Motivation

• These kind of algorithms require 2 things:– High number of sensors– High number of measurements

• It poses some problems– High computational complexity– Processing RAW data that may be not

necessary– It has to be done as close as real time as

possible.

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Motivation

• Compressive Sensing addresses the problem of having to deal with a large amount of Data.

• Particle Swarm Optimization is a good tool to match current activities to activities that have been learned before.

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Hardware Description

• In order to obtain data a set of sensors must be used.

• Due to time constraints, currently only an acceleration-gyroscopic sensor is going to be used.

• It must be able to recognize simple movements from the arm.

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Algorithm Description

Sparse Manifold

Conversion

Random Sampler

Accelerometer

Sampler

WHERE

WHO

WHAT

WHEN

HOW

PSO

MASTER MATRIX

SET

Identification Algorithm

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• The data is sampled from the sensors using a preset measurement matrix that proved to be successful with the control data.– It is one of the objectives to create

a Matrix that can handle all kind of data.

• In the sampler the data is redirected to one of the 5 income matrices.

Sparse Manifold

Conversion

Random Sampler

Accelerometer

Sampler

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• After the data has been retrieved, we will use PSO to find which of our current space solution best matches with the income data.

• Each Master Matrix will contain information on given movements, people, actions, and any other available recognition pattern.

WHERE

WHO

WHAT

WHEN

HOW

PSO

MASTER MATRIX

SET

Identification Algorithm

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Preliminary Results

• When capturing the signal, we present two possibilities.– Capture the signal without transforming the signal– Capturing the signal with previous Fourier

transformation.

• Each possibility had some good points and down points.– To much noise at the exit.– Some parts of the signal where not projected in the

output

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Preliminary Results

Original Signal

N=4001

Reconstruction

K=256

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Preliminary Results

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Conclusions

• The system presented a good reconstruction in the field of frequency, yet in the field of time it show to be a noisy signal.

• According to the results, we proved the algorithm can be applied to certain signals. But filtering needs to be done.

• The sampling part of the algorithm may not need to be as complex as compressive sensing since the signals are not that complex themselves.

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Future Work

• Tuning and testing of different source signals for different mappings.

• Giving a full justification to the CS solution.

• Implementing the Identification part of the algorithm.

• Implement the recognition matrices and see which parameters are to be set.

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a compressive sensing and swarm optimization algorithm for

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