Patent Publication Number: US-11375939-B2

Title: Biosignal acquisition method and algorithms for wearable devices

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of U.S. Provisional Patent Application 62/361,529, filed Jul. 13, 2016, which is incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     This invention relates generally to signal acquisition, and specifically to biological signal acquisition. 
     The work leading to this invention has received funding from the European Research Council under the European Union&#39;s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 335491. 
     BACKGROUND OF THE INVENTION 
     According to a 2014 study by Forbes, 71% of 16-to-24 year olds want wearable technology. Although at its beginning, the trend for using this technology is growing rapidly, allowing the users of wearable devices such as SmartWatch, Smart wristband, SmartCloth or Virtual Reality headsets to control electronic devices or monitor their physical parameters for entertainment or health care. However, one of the main drawbacks of present devices is their low signal quality and poor reliability due, for example, to the motion of the devices while in use. Furthermore, the number of sensing channels of the devices is limited by the cost, and reduced numbers of channels influences the signal quality. 
     SUMMARY OF THE INVENTION 
     An embodiment of the present invention provides apparatus, including: 
     a set of N electrodes, configured to be located in proximity to an epidermis of a subject, and to acquire signals generated by electric sources within the subject; 
     a set of M channels, configured to transfer the signals, where M is less than N; 
     a switch, configured to select, repetitively and randomly, M signals from the N electrodes and to direct the M signals to the M channels; and 
     a processor, configured to activate the switch, and to receive and analyze the M signals from the M channels so as to determine respective positions of the electric sources within the subject. 
     In a disclosed embodiment the processor is configured to determine respective amplitudes of the electric sources. 
     In a further disclosed embodiment the apparatus includes respective current sources, and the processor is configured to activate the switch so as to inject respective predetermined currents from the sources between selected pairs of the N electrodes. Typically, the injected currents have a plurality of baseband frequencies. The injected currents may have frequencies between 10 Hz and 100 GHz. 
     In a yet further disclosed embodiment the switch includes a matrix of switches. 
     In an alternative embodiment at least one of the electrodes is capacitively coupled to the epidermis. 
     In a further alternative embodiment the processor is configured to short-circuit together selected ones of the N electrodes. 
     In a yet further alternative embodiment the signals include sparse activations. 
     There is further provided, according to an embodiment of the present invention a method, including: 
     locating a set of N electrodes in proximity to an epidermis of a subject so as to acquire signals generated by electric sources within the subject; 
     transferring the signals via a set of M channels, where M is less than N; 
     selecting repetitively and randomly, M signals from the N electrodes, and directing the M signals to the M channels via a switch: and 
     activating the switch, and receiving and analyzing the M signals from the M channels so as to determine respective positions of the electric sources within the subject. 
     There is further provided, according to an embodiment of the present invention, a method, including: 
     positioning a set of N electrodes on an epidermis of a subject, wherein the electrodes are configured to acquire signals from the subject; 
     selecting a subset of the N electrodes that are in proximity with each other; 
     measuring impedances of the subset relative to each other; and 
     when the impedances change, using the change of impedances to estimate a change in the acquired signals, and applying the change in the acquired signals so as to correct the acquired signals. 
     In a disclosed embodiment, measuring the impedances includes injecting a predetermined signal into one of the subset, and measuring potentials of the acquired signals, generated in response to the injection, at remaining electrodes of the subset. 
     In a further disclosed embodiment a motion of the subject causes the change in the acquired signals. 
     In a yet further disclosed embodiment the signals originate from within the subject. 
     There is further provided, according to an embodiment of the present invention, a method, including: 
     positioning a set of N electrodes on an epidermis of a subject, wherein the electrodes are configured to acquire signals from the subject; 
     while the subject is performing an initial gesture, injecting a signal into the subject via at least one of the N electrodes, and measuring N respective potentials generated at the N electrodes in response to the injection; 
     formulating an initial matrix of the N respective potentials and the at least one of the N electrodes; 
     forming a correspondence between the initial matrix and the initial gesture; and 
     using the correspondence to recognize that a subsequent gesture of the subject corresponds to the initial gesture. 
     The method may also include injecting the signal into the subject via each of the N electrodes, and formulating the initial matrix as an N×N matrix of the N respective potentials and the N electrodes. 
     In a disclosed embodiment using the correspondence to recognize that the subsequent gesture of the subject corresponds to the initial gesture includes injecting the signal into the subject via the at least one of the N electrodes while the subsequent gesture is being performed, measuring further N respective potentials generated at the N electrodes in response to the injection, formulating a subsequent matrix of the further N respective potentials and the at least one of the N electrodes, and comparing the subsequent matrix with the initial matrix. 
     There is further provided, according to an embodiment of the present invention, apparatus, including: 
     a set of N electrodes configured to be positioned on an epidermis of a subject, wherein the electrodes are configured to acquire signals from the subject; 
     a switch connected to the set of N electrodes; and 
     a controller configured to: 
     operate the switch so as to select a subset of the N electrodes that are in proximity with each other, 
     measure impedances of the subset relative to each other, and 
     when the impedances change, use the change of impedances to estimate a change in the acquired signals, and apply the change in the acquired signals so as to correct the acquired signals. 
     Typically, measuring the impedances includes injecting a predetermined signal into one of the subset via the switch, and measuring potentials of the acquired signals, generated in response to the injection, via the switch at remaining electrodes of the subset. 
     There is further provided, according to an embodiment of the present invention apparatus, including: 
     a set of N electrodes configured to be positioned on an epidermis of a subject, wherein the electrodes are configured to acquire signals from the subject; 
     a switch connected to the set of N electrodes; and 
     a controller configured to: 
     while the subject is performing an initial gesture, inject a signal into the subject via at least one of the N electrodes, and measure N respective potentials generated at the N electrodes in response to the injection; 
     formulate an initial matrix of the N respective potentials and the at least one of the N electrodes; 
     form a correspondence between the initial matrix and the initial gesture; and 
     use the correspondence to recognize that a subsequent gesture of the subject corresponds to the initial gesture. 
     The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings in which: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of switching circuitry connected to electrodes attached to a subject, according to an embodiment of the present invention; 
         FIG. 2  is a schematic diagram of alternative switching circuitry, according to an embodiment of the present invention; 
         FIG. 3  is a flowchart of steps of an algorithm performed by a controller in reducing motion artifacts during acquisition of signals, according to an embodiment of the present invention; 
         FIG. 4  is a flowchart of steps of an algorithm performed by a controller in recognizing geometry or a gesture of subject, according to an embodiment of the present invention; 
         FIGS. 5-8  show activations of the brain, according to an embodiment of the present invention; and 
         FIG. 9  plots the ratio of the local body potential to the recorded potential vs. the electrode to body capacitive coupling, according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Overview 
     Recently there has been introduced a novel family of methods for signal acquisition and processing called compressive sensing. Compressive sensing is based on the observation that many signals in nature are “sparse” in some “basis.” The basis is herein called a dictionary, and it may be thought as a set of prototype signals. The signals in nature, referred to above, can be represented using a small number of the prototype signals, also termed elements or atoms, of this basis. Accordingly, sampling these signals using the Nyquist rate introduces redundancy. This observation permits developing mathematical theories for making use of this redundancy in both acquisition and processing of these signals to reduce the sampling frequency, memory requirements, and the power consumption of the acquisition and processing systems. 
     For realistic signals obeying some natural statistical properties, machine learning algorithms can be developed for both learning an optimal dictionary and learning signal decoding algorithms. Using this dictionary for the compressively sampled signals reduces the computational burden of signal restoration algorithms to levels suitable for the real time applications. 
     There is evidence showing that electrophysiological signals have a sparse nature. For instance, usually only a small fraction of our brain is active during a specific task. Consequently, embodiments of the present invention use mathematical ideas based on the modeling of the electromagnetic properties of biological signal propagation within biological tissues to provide a new method for biosignals acquisition, together with algorithms for their processing. In this method a controllable set of switches between the electrodes interfacing with the subject is altered in time during the electrophysiological signal acquisition and these combinations of signals lead into acquisition channels. 
     Not being restricted by the number of acquisition channels (which in our system is determined by the number of active sources rather than by the number of sensing elements as in a conventional design) using our method it is possible to place many sensing elements on a wristband for an electromyogram (EMG) or on a cap/helmet for an electroencephalogram (EEG) and still achieve an improved signal quality using a small number of A/D channels. We can achieve this by short-circuiting different numbers of sensing elements near the same sensing place, and in so doing we change the capacitive coupling between an equivalent electrode and the body. In addition, since the capacitive coupling depends on the distance of the electrodes from the body, our method enables encoding the mutual position of the sensor electrodes and the body, thus reducing any motion artifact. 
     (In general, we may place the sensing elements referred to above on any portion of the epidermis of a living creature.) 
     Moreover, there is ongoing research for gesture identification based on wrist shape identification. Accordingly, not only does the ability to track the relative position of the sensor electrodes and the body surface passively compensate for any motion artifact of the electrophysiological signal acquisition, but it also has a value in itself for a gesture recognition system. 
     Embodiments of the present invention use algorithms from the compressed sensing and machine learning families to extract new information that is not contained in prior art systems, while maintaining a low number of acquisition channels. Processing of this information increases the robustness of wearable devices to movement artifacts on the one hand, and reduces the number of the required measuring channels on the other hand. We thus increase the quality/cost ratio of the wearables, and also reduce the power consumption of wireless wearable devices leading to longer battery life. It will be understood that embodiments of the present invention may be advantageously used for medical devices, for instance by reducing the costs of present dense EEG systems (comprising many electrodes) and make embodiments using our invention affordable for any clinic. 
     In embodiments of the present invention that are configured for identifying gestures, a dictionary for different gestures is learned by following the temporal patterns of involved electric sources (e.g., muscles and the wrist contour shapes for EMG) and adapting the temporal patterns of switching circuitry. After proper modeling of the signal propagation within the biological tissues, and taking motion artifacts into account, the switches corresponding to the sensors most sensitive to the muscles involved in a relevant gesture will be more frequent in the temporal pattern of the switching circuitry. 
     The above description has assumed a passive acquisition of signals. However, the passive technique can be enriched by the active technique of electrical capacitance tomography (or in general electrical impedance tomography). In this technique currents are injected through electrodes around the body and measured voltages at other electrodes are used to estimate the internal impedance distribution. The active technique also improves the modelling of the electrophysiological signal propagation and enables discrimination between different geometries, i.e., gestures, of the body under test while recording electrophysiological signals. 
     DETAILED DESCRIPTION 
     Theory 
     EEG Inverse Problems 
     The electromagnetic activity of the brain is modeled by current dipoles within inhomogeneous conducting media. According to this modeling the gain matrix G of the EEG forward problem is calculated. The columns of G comprise the electrostatic potentials sampled at the sensors&#39; positions over the scalp induced by unit dipoles assumed to be placed in different locations and orientated perpendicularly to the human cortex. The inverse EEG problem aims to find the timecourses X of the current dipoles given the matrix of the measurements M=GX+E, where E represents the additive noise, and X is the variation of current dipoles amplitudes with time. Various regularization terms f(X) typically should be added to obtain meaningful solutions: 
     
       
         
           
             
               
                 
                   
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     The weighted minimum energy (wMNE) solution is obtained by imposing a weighted l 2  norm regularization 
     
       
         
           
             
               
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     This regularization typically leads to smeared solutions. It is more physiologically plausible to assume sparse activations of the brain cortex (i.e., a small fraction of the brain is activated at any given time) for realistic tasks. 
     Real Time l 1  Norm Minimization Algorithm 
     Ideally, the sparsity inducing norm is l 0  norm (minimizing the number of acting electric sources). However, the optimization problem of minimizing the l 0  norm regularization leads to a high computational burden that increases exponentially with the number of terms. As is well known, the l 1  norm regularization term 
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is also a sparsity inducing regularization term (being “sufficiently close” to the l 0  norm). To solve the optimization problem corresponding to the l 1  norm the following iterations have to be performed:
 
               X   0     =   0                 B     k   +   1       =     WM   +     SX   k                     X     k   +   1       =       π     λ   α       ⁡     (     B     k   +   1       )             
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                 prox     λ   ⁢           ⁢   ϕ       ⁡     (   X   )       =           π   λ     ⁡     (   a   )       r     =     {               max   ⁢     {     0   ,              X   r          2     -     λ   r         }                X   r          2       ⁢     x   r                      X   r          2     &gt;   0             0                  X   r          2     =   0                     
where r is a group index and the λ r  is the corresponding thresholding parameter of the given group.
 
     However, this iterative process requires much iteration for convergence. For relevant data (for instance, electrophysiological measurements corresponding to a given set of motions) the number of iterations can be truncated after a small number of steps used to learn the parameters defining each one of the iterations for relevant data (for instance, via stochastic gradient descent method). This method reduces the computational burden of the optimization process making it suitable for real-time applications. 
     Analog-to-Information Conversion 
     In order to recover reliably the distribution of the electrical potential on the scalp of a person usually about 100 electrodes are needed. However, the number of degrees of freedom (the number of active areas in the brain) for realistic tasks is typically much lower than the number of electrodes. It can be shown within the framework of compressed sensing theory that the number of the incoherent measurements that are needed to restore the original activation using the sparsity constraint is of the order of the degrees of freedom of this activation. Accordingly, an N-channel EEG (where N is the number of electrodes) can be multiplied by a quasirandom matrix resulting in an M-channel modified EEG where M&lt;N, while still being able to recover the electric sources of the brain activity (the same is applicable for other electrophysiological measurements). Moreover, the quasirandom matrix can be a quasirandom matrix of ones and zeros. 
     Hence, instead of using N analog-to-digital converters (ADC) we can use a set of switches (much cheaper than ADCs) and just M ADCs reducing both the cost and the power consumption of the system, as is described below with reference to  FIGS. 1 and 2 . In addition the Appendix below provides examples of simulations illustrating the use of a reduced number of ADCs, used in a quasirandom manner, to recover the electric sources of brain activity. 
     Capacitive Coupling 
     For medical devices conductive gel is used to establish good electrical between the skin and the measuring electrode. However, for consumable electronics devices it is inconvenient to use gel. Recently, another type of electrodes, dry electrodes, have emerged that do not need conductive gel. A dry electrode exploits the effect of capacitive coupling between the electrode and the conductive parts of the body where the signal is propagating. We briefly recall here the theory of capacitive coupling between ideal conductors in dielectrics that can be adapted to account for the capacitive coupling between an electrolyte (the conductive parts of the body) and the electrodes. 
     Given a 3D complex structure consisting of M conductors embedded in a uniform dielectric medium characterized by permittivity ε b . The capacitance matrix is defined by the relation 
     
       
         
           
             
               
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     Here we recall that for a parallel plate capacitor the capacitance is proportional to the plate area and inversely proportional to the distance between the plates. Accordingly, for the sensing electrode the coupling capacitance decreases with the distance between the electrode and the epidermis. Consequently, once the distance from the body to the electrode is kept substantially equal for all the sensing elements the capacitance should be proportional to the number of short-circuited electrodes, when the electrodes are switched, as described above. Since the signal at the input of the acquisition channel is divided between the input capacitance of the acquisition channel and the coupling capacitance of the electrode, the deviation from the linear dependence on the number of electrodes will correspond to the distance change from the electrode to the body. 
     Embodiments of the present invention use this fact to reduce the motion artifact of the electrode relative to the body. Moreover, assuming a relative rigidity of the signal acquisition device (for instance, a wristband) information about the relative position of the electrode and the body (deduced from the capacitive coupling of an electrode to the body) can be used to recognize a gesture (since the contour of the wrist can be related to the gesture of the subject). 
     The Appendix below provides more details of the effect of the coupling capacitance of electrodes on signals acquired by the electrodes. 
     Reference is now made to  FIG. 1 , which is a schematic diagram of switching circuitry  20  connected to electrodes attached to a subject, according to an embodiment of the present invention. 
     Switching circuitry  20  acts as a matrix of switches, and is coupled to a first plurality of N electrodes E 1 , E 2 , . . . E N , also referred to herein as electrodes  22 , which are in turn attached to be in proximity to an epidermis  24  of a subject. In the disclosure and in the claims, the term proximity, when referring to the attachment of the electrodes to the epidermis, is to be understood as the electrodes contacting the epidermis, and/or to be sufficiently close to the epidermis so as to be able to capacitively couple a measurable current to the epidermis. In one embodiment N=64, but there is substantially no limit on the number of electrodes that may be attached to circuitry  20 . Epidermis  24  is typically a scalp or a wrist of a subject, but the epidermis may comprise another surface of the subject, such as a leg or a finger. The switching circuitry is under overall control of a controller  28 , also herein termed a processor, which is typically an off-the-shelf processing unit, although in some embodiments processor  28  may at least partially comprise one or more dedicated components such as a field programmable gate array (FPGA) or an application specific integrated circuit (ASIC). 
     Switching circuitry  20  comprises a second plurality M of analog to digital converters (ADC 1 , . . . ADC M ), also referred to herein as ADCs  32 , providing digitized outputs. Circuitry  20  also comprises a third plurality K of current sources (I 1 , . . . I K ), also referred to herein as sources  36 . Circuitry  20  further comprises a controllable switch  40 , which, under control of controller  28 , is configured to switch between electrodes  22 , ADCs  32 , and current sources  36 . 
     The current sources provide the injection currents referred to above. The current sources are illustrated as having two leads, since any particular source may inject current between any selected pair of electrodes. Controllable switch  40  switches the ADCs and the electrodes, so that the ADCs acquire and digitize signals from selected electrodes  22 . Switch  40  also switches the current sources and the electrodes, so that sources  36  inject current into selected electrodes  22 . The currents are typically baseband, to increase capacitive coupling. Typically each current source may have a plurality of frequencies, so increasing the amount of information that may be extracted. In an alternative embodiment the frequencies are in the range of approximately 10 kHz-approximately 1 MHz, but frequencies outside this range are also possible, such as down to 10 Hz or up to 100 GHz. 
     There are a number of factors associated with circuitry  20 : 
     1) Selected electrodes  22  of interest only can be sampled reducing the number of ADCs  32  required. 
     2) Compressed sensing techniques can be applied by recording the combination of the measuring channels rather than each one independently. Examples of the use of these techniques are described above in the “Real time 11 norm minimization algorithm” and “Analog-to-information conversion” sections above. In one embodiment of the invention, the techniques may also be used in the flowchart of  FIG. 3 , as described below. 
     3) Capacitive coupling of the electrodes to the body can be determined by loading the electrodes with different capacitances to both update the modeling referred to above, thus improving the signal interpretation accuracy, and to discriminate between different body geometries classes (due to different gestures or different facial appearances, for instance). 
     4) Circuitry  20  enables application of electrical impedance tomography inducing the current through different pairs of electrodes  22  and measuring the resulting voltages on other electrodes  22 , (due to the possibility to encode the currents in different frequencies there is a possibility to induce a number of currents simultaneously). This allows updating an electrical model of the body near the measured bioelectric signals so as to reveal more information from these signals (which are confined to a low frequency region). 
     5) Circuitry  20  enables digitally toggling the measured and induced signals (to compensate for electrode movements between the sessions and to improve the classification accuracy). An example of toggling is provided in the description of the flowchart of  FIG. 3  below. 
     6) Circuitry  20  enables currents to be injected in parallel with signal measurements at any selected electrodes. Typically the injected current is in a narrow frequency band, so that both impedances and electrophysiological signals can be measured. 
       FIG. 2  is a schematic diagram of alternative switching circuitry  50 , according to an embodiment of the present invention. Alternative switching circuitry  50  comprises a microcontroller  54  which acts as a processor to operate the circuitry. In one embodiment microcontroller  54  is an Arduino Due microcontroller. Circuitry  50  is connected to electrodes  22  ( FIG. 1 ), which by way of example are assumed to comprise 128 electrodes. The connections to the electrodes are via eight electrode group connectors EG0 . . . EG7, herein also termed groups EG, which each connect to 16 electrodes  22 . Groups EG are driven by an electrode group driver  58 , which connects the electrodes to other elements of circuitry  50 , described below. 
     Driver  58  and groups EG are all individually controlled by microcontroller  54 , which enables the driver and the groups to access each of electrodes individually. The access enables the microcontroller to acquire signals from each of the electrodes, to inject signals into each of the electrodes, to connect electrodes together, as well as to insert impedances into lines leading to the electrodes. Thus driver  58  and groups EG act substantially as controllable switch  40  of circuitry  20  ( FIG. 1 ). 
     Analog signals from electrodes  22  are fed, via groups EG, to a set of eight amplifiers  62  followed by eight respective ADCs  66 , and microcontroller  54  acquires the digitized signals from the ADCs. Amplifiers  62  and ADCs  66  act substantially as ADCs  32  of circuitry  20 . 
     Circuitry  50  also comprises a single channel digital to analog converter (DAC)  70 , into which the microcontroller inputs digital signals so as to generate desired multiple analog signals. The multiple analog signals are demultiplexed in a demultiplexer (DMUX)  74 , and the resultant set of analog signals may be fed, via a line  76  and groups EG, to selected electrodes  22 . DAC  70  and DMUX  74  act substantially as current sources  36  of circuitry  20 . 
       FIG. 3  is a flowchart of steps of an algorithm performed by a controller in reducing motion artifacts during acquisition of signals, according to an embodiment of the present invention. For clarity, the steps of the flowchart are assumed to be implemented using circuitry  20  and controller  28  ( FIG. 1 ) and those having ordinary skill in the art will be able to adapt the following description, mutatis mutandis, if circuitry  50  and microcontroller  54  are used, or if any other circuitry having the characteristics of circuitries  20  and  50  is used. 
     Circuitry  20  and electrodes  22  are assumed to be installed in a device worn by a subject, herein also termed a wearable device. In an embodiment controller  28  is also installed in the wearable device. In an alternative embodiment controller  28  is remote from the device, such as being operative in a smartphone of the subject, and communicates with circuitry  20  either wirelessly or via optical or electrically conductive cables. 
     In an attachment step  80  electrodes  22  are attached in proximity to epidermis  24 . Herein, by way of example, the wearable device is assumed to be a wristband, and electrodes  22  are assumed to be affixed to the wristband, which a subject places on his/her wrist. 
     In a calibration step  82  of a calibration phase the subject is requested to remain stationary, and while the subject is stationary controller  28  measures impedances between pre-selected sets of electrodes in proximity to each other. The impedances are typically measured by the controller injecting known and measured currents into one of the pre-selected electrodes, and measuring the potentials generated in response at the other pre-selected electrodes using an ADC  32 . Controller  28  stores the impedances evaluated in step  82  as calibration impedances Z cal , and an indication may then be provided to the subject, for example by having a light, attached to the wristband, illuminate, that the calibration phase has completed. 
     In cases where the electrodes are not attached to the epidermis using gel, the impedances measured here typically have a capacitive component in an approximate range of tens of pF to 1 nF. 
     It will be understood that measuring impedances in this and other steps of the flowchart may comprise measuring the capacitive coupling of electrodes by shortcircuiting some of the electrodes. For example, for electrodes that are in relative close proximity to each other, and that can be assumed to have approximately equal capacitances (to the epidermis), shortcircuiting the electrodes, while measuring injected signals in the short-circuit and open-circuit stages, provides sufficient information to evaluate the capacitive coupling of each electrode. 
     The measured capacitances may be used in an adjustment step  90  of the flowchart, as described below. 
     Controller  28  then begins, in an operational step  84 , an operational phase. The controller  28  may indicate to the subject, for example by extinguishing the light illuminated in calibration step  82 , that the calibration phase has concluded and that the operational phase has commenced. At this point the controller begins acquiring signals from electrodes  22 , in one embodiment so as to recognize a gesture of the subject. An algorithm for recognizing a gesture, using electrodes  22 , is described below with reference to  FIG. 4 . While acquiring the signals, the controller continues to measure the impedances between the pre-selected electrodes, typically by substantially the same method as is described in step  82 . Typically, while checking and reducing motion artifacts, as described in the present flowchart, as well as recognizing a gesture, as described in the flowchart of  FIG. 4 , controller  28  toggles between the two processes. 
     In some embodiments, controller  28  may apply compressed sensing techniques, as described above, in acquiring signals from electrodes  22 . 
     In an iterative comparison step  86  the controller compares the measured impedances of the pre-selected electrodes with the impedance values stored in calibration step  82 , so as to check if there are any changes in impedance. If the comparison returns negative, i.e., there are no changes to the impedances, then the flowchart continues to a signal store step  88 , wherein the controller stores the signals acquired in step  84 . After store step  88  control of the flowchart returns to the beginning of step  86  so as to iterate the comparison. 
     If comparison step returns positive, i.e., the controller detects that there are changes ΔZ in the impedance values, the flowchart continues to a signal adjustment step  90 . The changes of impedance are typically due to motion of the electrodes relative to epidermis  24  of the subject. 
     In adjustment step  90  the controller calculates a ratio 
             R   =       Δ   ⁢           ⁢   Z       Z   cal             
and uses the value R of the ratio, as well as the values of impedances measured in step  82  and  84 , to adjust the value of the signal acquired in step  84 . The adjustment assumes a process of voltage division between an input impedance to ADC  32  and the capacitance of a given electrode (measured in step  84 ).
 
     In a storage step  92  the controller stores the adjusted signal values, which compensate for the changes in impedance induced by the electrode motion, and control of the flowchart returns to step  84 . 
       FIG. 4  is a flowchart of steps of an algorithm performed by a controller in recognizing geometry or a gesture of subject, according to an embodiment of the present invention. As for the flowchart of  FIG. 3 , the steps of this flowchart are assumed to be implemented using circuitry  20  and controller  28  ( FIG. 1 ). 
     In an attachment step  100  N electrodes  22 , where N is a positive integer, are attached in proximity to epidermis  24 . As for the flowchart of  FIG. 3 , the electrodes are assumed to be affixed to a wristband which a subject places on his/her wrist. 
     In a gesture indication step  102  the subject provides an indication to controller  28  of a gesture to be recognized by circuitry  20 . The indication may be provided to the controller by any convenient method known in the art. For example, the subject may tap on one of a number of gestures listed in a menu presented to the subject on the subject&#39;s smartphone. The controller stores the gesture indication as an index “ges”. 
     In a gesture performance step  104  the subject then performs the gesture, herein by way of example assumed to be the subject opening a clenched fist. While the gesture is being performed the controller  28  implements the following steps. 
     In an electrode selection step  106  the controller selects one of the N electrodes and injects current into the selected electrode. While the current is being injected the controller measures and acquires the potentials generated in response to the current injection on the other N−1 electrodes, as well as on the injection electrode. Typically a frequency of the current injected is approximately 40 kHz although any convenient frequency may be used. By using a specific injection frequency selected by the controller, the generated potentials on the N electrodes may be distinguished from other interfering signals. Typically, during the signal injection and potential value acquisition, the controller checks for motion artifacts and adjusts the acquired potentials as necessary, as explained above with respect to the flowchart of  FIG. 3 . 
     In a storage step  108  the controller stores the N measured potentials, adjusted to compensate for motion artifacts if necessary. 
     In a repetition step  110 , the controller repeats the actions of steps  106  and  108 . 
     In a final storage step  112  the controller formulates a square matrix [M] ges  of N electrodes×N acquired potentials. The controller stores matrix [M] ges  and gesture index ges in a gesture recognition table. 
     Typically the flowchart is repeated for a number of different gestures, generating respective matrices for each different gesture. Consequently, when the subject subsequently performs a gesture, the controller is able to access the gesture recognition table to recognize the gesture being performed. 
     While the description above has used as an example of a wearable device a wristband, it will be understood that the scope of the present invention is not limited to any particular type of wearable device, but rather includes any wearable device wherein circuitry such as circuitry  20 , and electrodes such as electrodes  22 , may be installed. For example, the wearable device may comprise an ankle band, a leg band, an arm band, a belt that is fixed around the waist of a subject, or a neck band. 
     The Appendix below provides examples of simulations performed by the inventors, using a simulation of circuitry  20 . In addition, the Appendix provides details of the effect of the coupling capacitance of electrodes on signals acquired by the electrodes. 
     Appendix 
     The Simulations 
       FIGS. 5-8  show activations of the brain, according to an embodiment of the present invention.  FIG. 5  shows an original activation of the brain in a region  200 . In this case we took a model of a brain comprising 300 sources and 64 electrodes in a standard 10-20 configuration. In what follows we show that using a random modulator the number of sensing electrodes can be reduced to 8. 
       FIG. 6  illustrates that, as expected, the original activation, at a region  210 , is easily recovered from the EEG using an I 1  norm. 
     For  FIG. 7  we multiply the  64  electrode EEG signal by a quasirandom 64×8 matrix of ones and zeros.  FIG. 7  illustrates that the activation is still resolved at a region  220 . 
     However, if we take 8 evenly distributed electrodes on the scalp and try to resolve the same activation, we can see in  FIG. 8  that it was not recognized correctly (instead of one focused activation at substantially identical regions  200 ,  210 , and  220  two focused activations emerged at different regions  230 ). 
     We conclude that random modulation of the signal permits reducing the number of electrodes without altering the solution quality. However, simply reducing the number of electrodes results in erroneous solutions. 
     Coupling Capacitance 
       FIG. 9  plots the ratio of the local body potential to the recorded potential vs. the electrode to body capacitive coupling, according to an embodiment of the present invention. The ratio is plotted for different input capacitances. 
     Here we explore the influence of the coupling capacitance for different numbers of electrodes and different input capacitance of the acquisition channel on the signal amplitude assuming a unit source. We assumed values of the input capacitances of the acquisition channel are in the range 10 pF-10 nF, and the range of the coupling capacitances of the electrode to the body is 30 pF-30 nF. 
     The figure shows that for a given input capacitance the input signal varies substantially when the capacitive coupling is altered. Hence by changing the number of electrodes switched to the given acquisition channel (and hence the capacitive coupling) the signal at the input is altered sufficiently to decode the relative position of the electrode and the body. 
     It will be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art.