9.5 Discussion
367
Fig. 9.14 (a) Initial image and (b) result of processing for a M-SCNN used for solving the task
“hole filling”
Remark 9.5 The examples discussed in Sect. 9.4 demonstrate that the class of MSCNNs has processing capabilities, in the (ϕ, q)-domain, similar to those displayed
by SCNNs [8] in the typical (v, i)-domain. This was confirmed by several other
numerical experiments where M-SCNNs have been applied to other kinds of
processing tasks. On this basis, we may conclude that it is potentially possible to
use the bulk of results already available in the literature for SCNNs (see, e.g., [9])
in order to design M-SCNNs for solving specific signal processing tasks.
Remark 9.6 Although from an abstract mathematical viewpoint the way a MSCNN processes signals is similar to that of a SCNN, since both NNs obey
analogous systems of differential equations, in practice there are some fundamental
differences. Indeed, the processing of a M-SCNN takes place in the (ϕ, q)-domain
so that voltages, currents and power drop off when a M-SCNN reaches a steady
state. This is an advantage in terms of power consumption with respect to SCNNs
[8] operating in the (v, i)-domain, where capacitor voltages, currents and power do
not vanish in steady state (as an example, see Fig. 9.12). We also remark that there
are basic differences in the way the result of computation is memorized. Indeed,
although a M-SCNN drops off in steady state, the memristors act as nonvolatile
memories keeping the result of computation, i.e., the asymptotic values of charges.
No battery is needed in a M-SCNN to hold the processing result. Quite on the
contrary, batteries are needed to hold in memory the processing result in a SCNN.
Remark 9.7 One main bottleneck of the classical Von Neumann architecture is that
processing and storing of information occur on physically distinct locations, such
as in the CPU and in the RAM. This limits the rate at which information can be
transferred and processed. A possible and promising way to overcome this issue
367
Fig. 9.14 (a) Initial image and (b) result of processing for a M-SCNN used for solving the task
“hole filling”
Remark 9.5 The examples discussed in Sect. 9.4 demonstrate that the class of MSCNNs has processing capabilities, in the (ϕ, q)-domain, similar to those displayed
by SCNNs [8] in the typical (v, i)-domain. This was confirmed by several other
numerical experiments where M-SCNNs have been applied to other kinds of
processing tasks. On this basis, we may conclude that it is potentially possible to
use the bulk of results already available in the literature for SCNNs (see, e.g., [9])
in order to design M-SCNNs for solving specific signal processing tasks.
Remark 9.6 Although from an abstract mathematical viewpoint the way a MSCNN processes signals is similar to that of a SCNN, since both NNs obey
analogous systems of differential equations, in practice there are some fundamental
differences. Indeed, the processing of a M-SCNN takes place in the (ϕ, q)-domain
so that voltages, currents and power drop off when a M-SCNN reaches a steady
state. This is an advantage in terms of power consumption with respect to SCNNs
[8] operating in the (v, i)-domain, where capacitor voltages, currents and power do
not vanish in steady state (as an example, see Fig. 9.12). We also remark that there
are basic differences in the way the result of computation is memorized. Indeed,
although a M-SCNN drops off in steady state, the memristors act as nonvolatile
memories keeping the result of computation, i.e., the asymptotic values of charges.
No battery is needed in a M-SCNN to hold the processing result. Quite on the
contrary, batteries are needed to hold in memory the processing result in a SCNN.
Remark 9.7 One main bottleneck of the classical Von Neumann architecture is that
processing and storing of information occur on physically distinct locations, such
as in the CPU and in the RAM. This limits the rate at which information can be
transferred and processed. A possible and promising way to overcome this issue