Optimization of multiplex measuring systems in the presence of statistical signal fluctuations

Kozlov, V. P.; Sedunov, E. V.

doi:10.1007/bf01291285

Cited by 1 publication

(5 citation statements)

References 3 publications

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“…We show an implication of constraints (24,25,26) on the SVs of W. This will allow us to better streamline (24,25,26) into Eq. (27), forming a lower bound on MSE.…”

Section: Conditions For a Global Optimummentioning

confidence: 82%

“…[22], this minimization was based on a numerical search of MSE, i.e., of Eqs. (23,24,25,26). However, Eq.…”

Section: Letmentioning

confidence: 99%

“…Let W be constrained by Eqs. (24,25,26). Then, C is an EV of W. Furthermore, let λ f be an EV of W. Then, |λ f | C. The proof is given in App.…”

Section: Conditions For a Global Optimummentioning

confidence: 99%

“…Thus, for a non-integer C, no matrix W is ideal, but a certain W can still be optimal, i.e. minimizing MSE within constraints (24,25,26).…”

Section: Consistency With Hadamard Matricesmentioning

confidence: 99%

“…The answer is no. The reason is that Eqs (24,25,26). bound the domain of W, hence bounding the domain of its SVs.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Optimal multiplexed sensing: bounds, conditions and a graph theory link

Ratner¹,

Schechner²,

Goldberg³

2007

Opt. Express

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Measuring an array of variables is central to many systems, including imagers (array of pixels), spectrometers (array of spectral bands) and lighting systems. Each of the measurements, however, is prone to noise and potential sensor saturation. It is recognized by a growing number of methods that such problems can be reduced by multiplexing the measured variables. In each measurement, multiple variables (radiation channels) are mixed (multiplexed) by a code. Then, after data acquisition, the variables are decoupled computationally in post processing. Potential benefits of the use of multiplexing include increased signal-to-noise ratio and accommodation of scene dynamic range. However, existing multiplexing schemes, including Hadamard-based codes, are inhibited by fundamental limits set by sensor saturation and Poisson distributed photon noise, which is scene dependent. There is thus a need to find optimal codes that best increase the signal to noise ratio, while accounting for these effects. Hence, this paper deals with the pursuit of such optimal measurements that avoid saturation and account for the signal dependency of noise. The paper derives lower bounds on the mean square error of demultiplexed variables. This is useful for assessing the optimality of numerically-searched multiplexing codes, thus expediting the numerical search. Furthermore, the paper states the necessary conditions for attaining the lower bounds by a general code.We show that graph theory can be harnessed for finding such ideal codes, by the use of strongly regular graphs.

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“…We show an implication of constraints (24,25,26) on the SVs of W. This will allow us to better streamline (24,25,26) into Eq. (27), forming a lower bound on MSE.…”

Section: Conditions For a Global Optimummentioning

confidence: 82%

“…[22], this minimization was based on a numerical search of MSE, i.e., of Eqs. (23,24,25,26). However, Eq.…”

Section: Letmentioning

confidence: 99%

“…Let W be constrained by Eqs. (24,25,26). Then, C is an EV of W. Furthermore, let λ f be an EV of W. Then, |λ f | C. The proof is given in App.…”

Section: Conditions For a Global Optimummentioning

confidence: 99%

“…Thus, for a non-integer C, no matrix W is ideal, but a certain W can still be optimal, i.e. minimizing MSE within constraints (24,25,26).…”

Section: Consistency With Hadamard Matricesmentioning

confidence: 99%

“…The answer is no. The reason is that Eqs (24,25,26). bound the domain of W, hence bounding the domain of its SVs.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Optimal multiplexed sensing: bounds, conditions and a graph theory link

Ratner¹,

Schechner²,

Goldberg³

2007

Opt. Express

View full text Add to dashboard Cite

show abstract

Optimization of multiplex measuring systems in the presence of statistical signal fluctuations

Cited by 1 publication

References 3 publications

Optimal multiplexed sensing: bounds, conditions and a graph theory link

Optimal multiplexed sensing: bounds, conditions and a graph theory link

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