Get Cellular Neural Networks: Analysis, Design and Optimization PDF

By Martin Hänggi, George S. Moschytz

ISBN-10: 1441949887

ISBN-13: 9781441949882

ISBN-10: 1475732201

ISBN-13: 9781475732207

Cellular Neural Networks (CNNs) represent a category of nonlinear, recurrent and in the community coupled arrays of exact dynamical cells that function in parallel. ANALOG chips are being constructed to be used in purposes the place subtle sign processing at low energy intake is needed.
sign processing through CNNs in basic terms turns into effective if the community is carried out in analog undefined. In view of the actual barriers that analog implementations entail, strong operation of a CNN chip with recognize to parameter diversifications should be insured. by way of some distance now not all mathematically attainable CNN projects should be performed reliably on an analog chip; a few of them are inherently too delicate. This ebook defines a robustness degree to quantify the measure of robustness and proposes a precise and direct analytical layout procedure for the synthesis of optimally strong community parameters. the strategy relies on a layout centering method that's commonly appropriate the place linear constraints need to be chuffed in an optimal manner.
Processing velocity is usually an important whilst discussing signal-processing units. on the subject of the CNN, it's proven that the environment time may be laid out in closed analytical expressions, which allows, at the one hand, parameter optimization with appreciate to hurry and, nevertheless, effective numerical integration of CNNs. Interdependence among robustness and pace matters also are addressed. one other aim pursued is the unification of the idea of continuous-time and discrete-time platforms. via a delta-operator procedure, it truly is confirmed that a similar community parameters can be utilized for either one of those periods, no matter if their nonlinear output capabilities fluctuate.
extra advanced CNN optimization difficulties that can not be solved analytically necessitate resorting to numerical equipment. between those, stochastic optimization options reminiscent of genetic algorithms turn out their usefulness, for instance in snapshot category difficulties. because the inception of the CNN, the matter of discovering the community parameters for a wanted activity has been considered as a studying or education challenge, and computationally pricey tools derived from commonplace neural networks were utilized. moreover, a variety of worthwhile parameter units were derived by way of instinct.
during this publication, an immediate and particular analytical layout process for the community parameters is gifted. The procedure yields ideas that are optimal with recognize to robustness, a facet that is the most important for winning implementation of the analog CNN that has frequently been overlooked.
`This fantastically rounded paintings presents many fascinating and beneficial effects, for either CNN theorists and circuit designers.'
Leon O. Chua

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With the result from the previous section, it is now easily seen that optimization with respect to relative robustness implies increasing y (p), while keeping II p III small. Template scaling by large factors does not improve the robustness significantly, and has the disadvantage of resulting in larger template values which may not be realizable on the CNN chip. The design of a template with maximum robustness is in fact a design centering problem, since Popt is, in some sense, "centered" in :R.

2: The sets of programmable template values. 5, ... 5, ... , the initial state has to be set. The current sources for the A, B, and I weights are switched off for t < 0, and the resistor is disconnected. C is charged to an initial value xi) (0). At t = 0, the current sources and R are reconnected. Nearly any implementation of controlled current sources is likely to exhibit random offset currents, and the total offset current will not be negligible. To charge the capacitor and to cancel the offset current, additional circuitry is required which is realized by an operational amplifier and a SamplelHold.

5) CHAPTER 4. CNN SETTLING TIME 50 The settling times are obtained by solving xi+(Ti) = +1 and xi-(Ts-) = -1. 6) and, for ac = 1, + Ts = 1 -Xi+(O) Wi+ Note that Wi+ > 0, Wi- < 0, Xi+ can now be expressed as ; Ts- - E {-I ,O}, -1-x'-(O) I and Xi- WiE . 7) {O, I}. The settling time However, these analytical results depend on the input image and on the initial states; they do not allow the prediction of Ts if this information is not available. 3) by maximizations over all possible combinations of neighboring cells and initial conditions.

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Cellular Neural Networks: Analysis, Design and Optimization by Martin Hänggi, George S. Moschytz


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