Patent Description:
Various known methods were proposed to facilitate remote diagnosis of medical conditions, such as heart problems. For example, South Korean Patent <CIT> describes an electrocardiogram sensing apparatus comprising: (a) an electrocardiogram sensing unit for measuring a user's electrocardiogram signal; a processor for filtering the measured electrocardiogram signal using a bandpass filter and for compressing and sensing the filtered electrocardiogram signal; and a data communication unit for transmitting the compressed sensed electrocardiogram signal to the electrocardiogram monitoring device; (b) a first communication unit for receiving the compression sensed electrocardiogram signal; a processor for restoring the compressively sensed electrocardiogram signal and analyzing the restored electrocardiogram signal; and a display unit for outputting the electrocardiogram analysis data; and (c) an electrocardiogram monitoring apparatus.

Weighted mixed-norm minimization based joint compressed sensing recovery of multi-channel electrocardiogram signals is discussed by <NPL>.

An embodiment of the present invention that is described hereinafter provides an apparatus according to claim <NUM>.

There is further provided, in accordance with another embodiment of the present invention, a method according to claim <NUM>.

Some electrophysiological (EP) disorders, such as cardiac arrhythmia and epileptic seizures, may be manifested in occasional episodes of rapidly varying EP signals, such as electrograms or electroencephalograms, respectively, which may appear irregular. Early detection and characterization of such cardiac or brain disorders is not straightforward and poses difficulties to the clinician.

Acquiring analog EP signals (also called hereinafter "waveforms") with a high spatiotemporal resolution, either invasively (e.g., using an implant or a catheter to acquire atrial electrograms), or using electrodes attached to skin (e.g., to acquire electroencephalograms), are a promising approach for early detection of such disorders.

For example, to detect cardiac arrhythmia, e.g., atrial fibrillation (AF), electrograms of diagnostic value may be acquired by a dense multi-electrode array (e.g., an implanted electrode array), normally for time periods ranging from <NUM> seconds to several minutes. However, this generates extremely large quantities of raw multi-channel data that are difficult to manage, record, and wirelessly transmit, in particular by low-power devices, such as a wearable unit coupled to an implanted electrode array.

Moreover, the high data rates required for transmitting electrograms/electroencephalograms (e.g., from a wearable acquisition module connected to an electrode array implant to a base station) are expensive in terms of power consumption and resources, making the use of an implant or a wearable module for early diagnosis of some arrhythmias impractical.

While existing methods of data compression may assist in reducing data volumes of regular EP signals, such as of sinus rhythms, electrogram signals that are irregular during arrhythmia cannot be sufficiently compressed with such methods, and, by the nature of arrhythmia, there is no way of knowing whether data compression of chaotic electrogram signals is sufficiently accurate, which may lead to loss of vulnerable data.

Compressed sensing (CS) is a promising approach to achieve data compression of EP signals, such as occurring during arrhythmia or epileptic seizure. In essence, CS is a linear programming optimization problem that attempts to span a waveform (i.e., the analog signal) with a minimal number of base-functions, below the Nyquist rate of the waveform. The spanning, which is approximate, is done by iteratively approximating a solution for a linear system of equations, by minimizing a norm. The approach requires individual waveforms to be sparse. The approach further requires incoherence between a sensing matrix Φ and a representation matrix Ψ made of a linear basis of vectors in which the signal is sparse. The "restricted isometry property" (RIP) characterizes the sensing matrix which is nearly orthonormal while operating on sparse vectors. A widely used norm in CS is the ℓ<NUM> norm, defined below.

The present invention uses the high spatiotemporal correlation at which the electrograms are acquired (e.g., with some form of sufficiently dense electrode array), to perform compressed sensing (CS) of the multiple-electrogram data with a higher compression ratio (CR) than is possible by standard CS methods.

The high spatiotemporal correlation enables spanning (e.g., representing) waveforms (e.g., electrograms) at a same accuracy using fewer base-functions than with standard CS methods. At least some of the electrograms, e.g., the spatiotemporally correlated ones, require fewer base-functions to span by minimizing a mixed-norm ℓ<NUM>,<NUM>, defined below, which is built using the aforementioned spatiotemporal correlations.

In particular, knowing electrode array geometry, i.e., the positions of the sensing electrodes of the array relative to one another, enables the use of spatiotemporal correlations in the multi-channel electrograms to better CS the signals. In particular, using CS of the spatiotemporally-correlated signals, enables significant compression of the multi-channel electrograms without impacting the quality of data reconstructed from the compressed data (e.g., an SNR of the reconstructed data), and the clinical ability to use the data for diagnostic purposes.

In particular, using the disclosed mixed-norm ℓ<NUM>,<NUM> yields higher CR per given (e.g., predefined) SNR, or same CR with higher SNR, than achievable using the widely used in CS ℓ<NUM> norm.

In an exemplary embodiment, an apparatus is provided, that includes data acquisition circuitry and a processor. The data acquisition circuitry is configured to acquire multiple signals using multiple respective electrodes of an array of electrodes coupled to an organ of a patient. The processor is configured to (a) hold a definition of a mixed-norm, such as mixed-norm ℓ<NUM>,<NUM>, that is defined as a function of relative positions of the electrodes in the array, and (b) jointly compress the multiple signals in a compressed-sensing (CS) process that minimizes the mixed-norm.

Additionally, or alternatively to the above spatiotemporal property, in exemplary embodiments, electrograms can be CS using a method called "rakeness. " In the rakeness CS method, each electrogram is preprocessed by multiplying it with a pseudo-random code, comprising a time-sequence of "<NUM>", "<NUM>", and "-<NUM>". The operation of rakeness improves compression as follows: applying rakeness exploits the energy distribution in the waveform to increase a correlation of the electrogram waveform with a pseudo-random code configured to have the temporal statistics of the analog signal (i.e., correlated with a matrix comprising of {-<NUM>, <NUM>, +<NUM>} values with similar statistical distribution as the electrogram waveform). The latter property is also called the aforementioned "restricted isometry property (RIP)," or "incoherence. " This property enables to solve the electrogram waveform representation problem "accurately enough" with fewer base-functions than required without rakeness, and thus allows increasing CR while maintaining SNR. "Accurately enough" in CS usually means both in the ℓ<NUM> norm and the mixed-norm ℓ<NUM>,<NUM> minimization sense.

When using rakeness, the pseudo-random code and the input electrogram have similar energy spectra, and thus can capitalize on the temporal correlation that exists between them. Rakeness requires, and takes advantage of, sparsity of the multi-channel electrogram signals in both the spatial domain and the time domain.

The aforementioned data acquisition circuitry is further configured to apply respective pseudo-random sequences to the signals so as to increase sparsity of the signals (a sparsity linear space is spanned by a basis in which the signal is sparse. In that basis, representation matrix Ψ represents a "symlet" discrete wavelet transform), and wherein the processor is configured to minimize the mixed-norm for the signals having the increased sparsity and incoherence.

In another exemplary embodiment, the data acquisition circuitry comprises a single analog-to-digital convertor (ADC) configured to convert the multiple signals into digital signals, after rakeness was incorporated to each of these and, subsequently, the signals were multiplexed.

By utilizing spatiotemporally-correlated electrograms and/or rakeness-processed electrograms, a signal compressed by compressed sensing can be reconstructed with a better SNR, which allows for either a higher CR (enabling, for example, reduction of the required mobile transmission bandwidth), or for a better SNR for a given CR, compared with using conventional compressed sensing methods.

In some exemplary embodiments, an acquisition circuitry is provided to perform the rakeness using, for example, a pseudo-random binary sequence (PRBS) generator to provide the "<NUM>", "<NUM>", and "-<NUM>" sequenced signals. As noted above, rakeness-based CS allows for higher data rates to be transmitted (e.g., wirelessly) using low-power electronic resources, making such circuitries suitable, for example, for an implantable-wearable combo device, or for remote bandwidth-limited communication links (e.g., bandwidth-limited cellular links).

Moreover, more efficient decoding circuitry can be provided, e.g., inside a remote wireless device, to decompress the data (e.g., reconstruct the compressed data), and therefore, regardless of the acquisition technique (e.g., implant or catheter, local wireless or wired transmission), the compressed-sensing data can be wirelessly transferred to reconstruction in the remote wireless devices (e.g., a tablet with a cellular communication capability), for remote diagnosis.

In an exemplary embodiment, the aforementioned apparatus further comprises a wireless unit configured to transmit the compressed signals to a base station. In another embodiment, the apparatus further comprises a wearable package containing the data acquisition circuitry and the processor.

In some exemplary embodiments, the measurement matrix comprising of {-<NUM>, <NUM>, +<NUM>} values, which represents essentially a modulation operation, is used in order to suppress "<NUM>/f" acquisition noise and offset. The suppression of the <NUM>/f noise and offset further reduces requirements from the acquisition circuitry and makes its miniaturization more feasible, e.g., for use in an implant or a wearable device.

Exemplary embodiments of the present invention pertain to using various forms and types of electrode arrays, such as those disposed on catheters, including, for example, basket, Pentaray™, multi-finger or multi-spline arrays such as a Picasso™ design, and any high-density grid array of known inter-electrode distances.

By providing highly efficient compressed sensing and reconstruction methods of arrhythmogenic signals, practical early-detection arrhythmia or epileptic-seizure monitoring devices may become available, and, furthermore, remote diagnosis may become more readily at hand. The present invention is particularly applicable for disease states in the electrophysiology field such as atrial fibrillation and ventricular fibrillation through the use of the aforementioned novel systems, methods, and algorithms to facilitate EP signal processing, planning, and diagnosis.

As noted above, different types of medical devices, e.g., implants or catheters, may be used to invasively acquire multi-channel electrogram data with high spatiotemporal resolution. <FIG> and <FIG> describe CS of catheter-acquired electrograms, whereas <FIG> describes CS of an implant-wearable combo device acquired electrograms. The two exemplary embodiments differ mainly in their different communication bottlenecks and power constraints that are overcome by the disclosed spatiotemporally correlated and rakeness-processed compressed sensing methods.

For example, with a catheterization system shown in <FIG>, local acquisition and communication resources may be large enough and the compressed sensing be more critical for the remotely transmission, downloading and decoding of the medical data, as shown in <FIG>. With the implant-wearable combo device shown in <FIG>, local acquisition and communication resources are typically highly limited in the lightweight and small size combo device, and the disclosed methods are initially applied to solve these particular limitations.

<FIG> is a schematic, pictorial illustration of a system <NUM> for electrophysiological (EP) mapping. <FIG> depicts a physician <NUM> using an EP mapping catheter <NUM> to perform an EP mapping of a heart <NUM> of a patient <NUM>. Catheter <NUM> comprises, at its distal end, a multi-channel electrode array <NUM> comprising one or more arms <NUM>, each of which coupled to mapping-electrodes <NUM>. During the mapping procedure, electrodes <NUM> acquire and/or inject signals from and/or to the tissue of heart <NUM>. In particular, electrodes <NUM> acquire intra-cardiac EP signals, such as atrial electrograms (AEG).

The respective locations of mapping-electrodes <NUM> inside heart <NUM> (i.e., where the intra-cardiac ECG signals are measured) are tracked as well, so that the processor may link each acquired electrogram with the location at which the signal was acquired. System <NUM> externally senses electrical position signals and EP data, such as electrograms (ECG), using a plurality of external electrodes <NUM> coupled to the body of patient <NUM>; for example, three external electrodes <NUM> may be coupled to the patient's chest, and another three external electrodes may be coupled to the patient's back. For ease of illustration, only one external electrode is shown in <FIG>.

An example of a system capable of using the sensed electrical position signals to track the locations of mapping-electrodes <NUM> inside heart <NUM> of the patient is the CARTO®<NUM> system (produced by Biosense Webster, Irvine, California). The CARTO®<NUM> system uses a tracking method named Advanced Current Location (ACL), which is described in detail in <CIT>.

A data acquisition module <NUM> receives the multiple electrogram signals conveyed to an electrical interface <NUM> over a wire link that runs in catheter <NUM>. Using the sensed positions to establish spatiotemporal correlations between electrograms, and using the aforementioned rakeness method, a processor <NUM> performs compressed sensing on the AEG data contained in these signals. Processor <NUM> stores the compressed sensing electrograms in a memory <NUM>, and later the CS signals are wirelessly communicated to a remote site (as shown in <FIG>). In parallel, processor <NUM> may present the electrogram traces <NUM> on a display <NUM> of system <NUM>.

The exemplary illustration shown in <FIG> is chosen purely for the sake of conceptual clarity. Other types of multi-electrode sensing geometries, such as of the Lasso® catheter (produced by Biosense Webster) may also be employed. Additionally, contact sensors may be fitted at the distal end of electro-anatomical catheter <NUM> and transmit data indicative of the physical quality of electrode contact with tissue. In an exemplary embodiment, measurements of some electrodes <NUM> may be discarded because their physical contact quality is poor, and the measurements of other electrodes may be regarded as valid because their contact quality is high.

Processor <NUM> typically comprises a general-purpose computer with software programmed to carry out the functions described herein. The software may be downloaded to the computer in electronic form, over a network, for example, or it may, alternatively or additionally, be provided and/or stored on non-transitory tangible media, such as magnetic, optical, or electronic memory. In particular, processor <NUM> runs a dedicated algorithm that enables processor <NUM> to perform the steps described in <FIG>.

While the exemplary embodiment shown in <FIG> shows the processor used for CS external to module <NUM>, in other embodiments, module <NUM> has its own processor to perform compressed sensing on the spatiotemporally correlated and/or rakeness-processed electrograms.

<FIG> is a block diagram that schematically illustrates a workflow in which electrograms are acquired and undergo compressed sensing (CS) by system <NUM> of <FIG>, and afterwards remotely communicated and reconstructed.

As seen, the multiple electrogram data is locally communicated using a wire link <NUM> (e.g., that runs inside catheter <NUM>) and (local) processor <NUM> performs compressed sensing on the spatiotemporally-correlated and/or rakeness-processed data. Physician <NUM> may inspect the data graphically on local display <NUM>, for example, to evaluate a clinical relevance of the data.

In the illustrated exemplary embodiment, processor <NUM> is connected to a network <NUM> by a network interface, such as a network interface card (NIC) <NUM>, and a link <NUM>, which it uses to transmit the compressed sensing electrogram traces to a remote wireless device (e.g., a tablet) <NUM>.

Compressed data may be first uploaded to a network <NUM> with link <NUM> supporting, for example, an upload rate of several megabit/sec, nowadays considered a limited rate. In an exemplary embodiment, wireless device <NUM> is bidirectionally connected to network <NUM> via an NIC <NUM> and a link <NUM>. Wireless device <NUM> receives the compressed sensing electrogram traces and decompresses them using its processor <NUM> that furthermore presents the decompressed data on its display <NUM> (e.g., a tablet display). A medical expert may view the ECG traces <NUM> on display <NUM> and provide diagnosis from a distant location having limited access to communications (e.g., cellular only).

<FIG> is a schematic system-level diagram with a flow chart of an implanted-wearable combo device <NUM>/<NUM> for compressed sensing (CS) and wireless transmission of electrograms, and of a base station <NUM> receiving the CS electrograms. As seen, a multi-channel electrode array implant <NUM> is located at a left atrium of heart <NUM>. The array is connected by wires to a wearable data acquisition and wireless transmission module <NUM>, which communicates with a base station <NUM> over a communication link <NUM>.

Module <NUM> includes circuitry and a processor that enables the module to efficiently perform compressed sensing on the electrograms acquired by electrode array implant <NUM>, utilizing spatiotemporally-correlated electrograms and/or rakeness-processed electrograms. Despite module <NUM>'s limited power source (e.g., a battery), the module is capable of acquiring and transmitting the AEG data at acceptable rates to a base station <NUM> by using the disclosed CS techniques.

For example, using an electrode array with an inter-electrode distance of <NUM> to acquire signals, electrograms from at least <NUM> recording sites have to be CS, to cover an entire atrium, including the right atrium, the left atrium, and the Bachmann bundle. To record the signals from <NUM> electrodes at a resolution of <NUM> bits and a sampling frequency of <NUM>, the total data rate required is <NUM> × <NUM> × <NUM> × <NUM>, or <NUM> Mbit/s, resulting in ≈ <NUM> Gbit/min. Restricting recording sites to a left atrium still results in a several Gbit/min data rate (i.e., on the order of <NUM> Mbit/sec).

The disclosed CS technique has to provide high CR, e.g., a CR above <NUM>, to enable using remote devices with bandwidth-limited communication links. The high CR is further important to save battery power so such devices are available for patients to wear. A CR for digital signals can be estimated as a ratio of number of samples multiplied by number of bits. Therefore, a CR value of, e.g., <NUM>, can be achieved by compressing the number of samples, e.g., from <NUM> to <NUM>, and the number of bits, e.g., from <NUM> to <NUM>.

In <FIG>, base station <NUM> has the compressed sensing data downloaded using a wireless receiver, and the signal is consequently reconstructed (<NUM>), stored (<NUM>), and further processed (<NUM>), for example, for logging, visual presentation, and user alerts.

<FIG> is a flow chart that schematically describes a method for spatiotemporally correlated and rakeness-processed compressed sensing (CS) of electrograms.

The algorithm, according to the presented exemplary embodiment, carries out a process that begins at a data receiving step <NUM>, in which a data acquisition module, such as module <NUM> of <FIG>, or module <NUM> of <FIG>, receives multiple electrograms acquired by an electrode array, as described above.

The data acquisition module further receives locations of the electrodes at which the electrograms were acquired, at a receiving locations step <NUM>. The locations are measured by any known method, such as by position tracking of a catheter, or by a prespecified map for an implant. The locations may be provided as relative positional relations (e.g., relative locations on a given grid). A processor, at least one of which, in the flow chart of <FIG>, is assumed to be included among the data acquisition modules, performs all subsequent local processor-related steps using the received (e.g., uploaded as a table) locations, such as described in the following steps.

Next, at a spatiotemporal correlation identification step <NUM>, each processor of a data acquisition module identifies electrograms that are spatiotemporally correlated based on their positions in the array (e.g., based on a relative distance between electrodes).

At a rakeness step <NUM>, each processor of the data acquisition module applies rakeness to the electrograms. The motivation behind using rakeness is that, with real life signals, it is possible to reduce the reconstruction error ∥x-x̂∥ after the solution of Eq. <NUM> below by identifying second-order correlations between signals (e.g., electrograms).

Rakeness ρ between two electrograms u and v can be defined as ρ(u, v) = Eu,v[|〈u, v〉|<NUM>], where Eu,v refers to the expectation with respect to the two vectors and ρ maximizes the signal energy for most correlated vectors. In this method, each signal xj is preprocessed by multiplying it with a different pseudo-random code (i.e., unique per signal xj), comprising a sequence of "<NUM>", "<NUM>", and "-<NUM>". The code incorporates the input statistics and thus capitalizes on the correlation that exists (i.e., pseudorandom-code-imposed correlation) between the input signal and the code to identify correlation among electrograms and the pseudo-random code. In conclusion, in an exemplary embodiment, a processor reconstructs the input signal by using mixed-norm recovery algorithm which takes into account signals energies, so as to achieve better reconstruction performance (e.g., in SNR or CR senses). Details of the rakeness-based compressed sensing method can be found in "<NPL>.

After steps <NUM> and/or <NUM> are performed to identify spatiotemporal correlations between electrograms and to rakeness-process the electrograms, each processor of the data acquisition module performs compressed sensing on the electrograms, at a compressed sensing step <NUM>, using either spatiotemporally-correlated electrograms identified as such (e.g., having a degree of correlation ranging above a prespecified absolute value threshold, in that sense a maximal degree of correlation of +<NUM> and -<NUM> are considered both maximal) or both spatiotemporally-correlated electrograms and rakeness-processed electrograms. Gaining on steps <NUM> and/or <NUM>, the processor can compress the multi-channel electrograms with higher CR without compromising quality of data subsequently reconstructed from the compressed data (e.g., without degrading an SNR of the reconstructed data).

CS based on spatiotemporal correlations is performed by minimizing the ℓ<NUM>,<NUM> norm as described in brief below:
Consider a 2D array of L electrodes where the signal X is acquired from various channels with a sensing matrix Φ and the measurement matrix Y which can be described as Y = ΦX + n, where n is the measurement noise, modeled as spatiotemporally white Gaussian noise. In the measurement vector, X, X = [x<NUM>,x<NUM>,. ,xL ], each xj component is the timedependent signal acquired from the j-th single electrode. Let also A = [α<NUM>, α<NUM>,. ,αL ] the matrix composed by the sparse representation vectors of [x<NUM>, x<NUM>,. , xL ], with xj = ψαj, j=<NUM>, <NUM>,. L, or, with a more compact notation, X = ψA. In matrix A, given that the signal x is K-sparse in an arbitrary basis ψ=[ψ<NUM>, ψ<NUM>,. ψN], x can be represented as x = ψα, where α is an N-dimensional vector with only K<<N nonzero elements in the matrix ψ. K and N are related by sparsity which is given by (<NUM>-K/N) -<NUM>%.

From the compressed measurement samples, the signal can be reconstructed by solving the minimization problem given by <MAT> where ∥α∥<NUM> is the ℓ<NUM> norm of the signal. Further, the reconstructed input signal is given by x̂ =ψα̂.

The multi-channel atrial electrograms share similarities among the adjacent channels, which can be exploited for an improved reconstruction performance. Multi-channel CS acquisition can be formulated as a multiple-measurement vector (MMV) problem and can be solved with jointly sparse recovery algorithms. The aim of MMV compressed sensing is to recover the jointly sparse A, which can be formulated as <MAT> where the joint sparsity in A is induced by the ℓ<NUM>,<NUM> mixed-norm defined by <MAT>, meaning finding most correlated electrograms by minimizing the mixed-norm ∥A∥<NUM>,<NUM>. Details of the rakeness-based compressed sensing (rak-CS) method can be found in the aforementioned paper by <NPL>.

Finally, at a compressed sensing data transmission step <NUM>, the compressed sensing EP data is wirelessly transmitted, for example, from a wearable data acquisition module to a base station.

The following sections compare SNR of reconstructed electrograms for the cases of (a) using rakeness vs. using standard CS, and (b) using mixed-norm ℓ<NUM>,<NUM> vs. using ℓ<NUM> norm. The SNR results were compared using same numbers of base functions (i.e., linear basis dimensions), meaning for same CR values.

In a demonstration of the disclosed techniques, atrial electrograms were recorded on the epicardium, the surface of the heart, using a <NUM> by <NUM> flexible multi-electrode array with <NUM> gold-plated electrodes and a <NUM>-channel data-acquisition system. The data was acquired using analog front-end signal acquisition circuitry consisting of an amplifier with a gain of <NUM> dB, a bandpass filter with the bandwidth extending from <NUM> to <NUM>, and an analog-to-digital converter with a resolution of <NUM> bits, which sampled the analog signal at <NUM>. A total of <NUM> electrode-array sections were required to cover the entire surface area of the atria. For rakeness-based CS (rak-CS), one of the recorded sections was used as a reference for the correlation matrix estimation.

Using an ℓ<NUM> norm, a compressed sensing code decodes and reconstructs the signals by solving Eqs. <NUM> and <NUM>, using a wavelet transformation basis. The reconstructed signal is compared to the original signal using the performance metric, reconstruction signal-to-noise ratio (RSNR) given by <MAT>.

The reconstruction performance, i.e., the average RSNR (ARSNR) as a function of CR, of a standard compressed sensing (CS) method that minimizes only the ℓ<NUM> norm without preferred choice of electrograms, is compared with reconstruction performance of mixed-norm ℓ<NUM>,<NUM> compressed sensing recovery approach (the aforementioned MMV) that minimizes the ℓ<NUM> norm for spatiotemporally-correlated electrograms.

<FIG> are graphs of spatial-domain and time-domain average reconstructed SNR of (ARSNR) of electrogram signals as a function of CR for signals with compressed sensing (CS) both with and without rakeness.

<FIG> show two CS approaches, standard CS (<NUM>) and rak-CS (<NUM>) on a data set, composed of real medical recordings. The performance of rak-CS (<NUM>) is better than standard CS (<NUM>), especially at higher compression ratios. In particular, the difference in the achieved ARSNR in rak-CS and standard CS, for CR = <NUM>, in the time domain, is <NUM> dB for AF waveforms.

In <FIG>, the multi-channel data is modeled as a multiple-measurement-vector problem and the mixed-norm is used to exploit the group structure of the signals in the spatial domain to obtain improved reconstruction performance (<NUM>)over ℓ<NUM> norm minimization performance (<NUM>). Using the mixed-norm recovery approach, for CR = <NUM>, the difference in achieved ARSNR performance between rak-CS and standard CS is <NUM> dB for AF.

Moreover, without any use of rakeness, the ℓ<NUM>,<NUM> mixed-norm recovery approach yields by itself, as <FIG> shows for CR = <NUM>, a <NUM> dB better ARSNR (<NUM>) than that achieved using ℓ<NUM> norm. Therefore, providing the relative positions to use spatiotemporal correlations between the multiple electrogram signals enables the compressed sensing of the multiple electrogram signals with a given CR (e.g., <NUM>), such that the compressed signals yield reconstructed signals having a superior SNR compared with a method not using the aforementioned spatiotemporal correlations presented by signals acquired using dense electrode grids.

<FIG> are graphs of spatial-domain and time-domain rakeness-based compressed-sensed (rak-CS) signals after being reconstructed vs. the original recorded electrogram signals. The reconstruction waveforms were lowpass filtered (up to <NUM>), making the waveforms look less noisy and thus easier to analyze by a physician.

<FIG> shows the reconstruction of the atrial electrograms in the time domain during AF for an arbitrarily selected channel number (ch = <NUM>) out of <NUM> recorded channels. <FIG> shows the reconstruction of the AEGs in the spatial domain, during AF, for an arbitrarily chosen time instant. As seen, the rak-CS reconstruction of the signal adds high frequency noise in the time-domain. However, this noise does not distort the signal and can be largely removed by standard signal processing methods.

In parallel to algorithmic tools, embodiments of the present invention offer data acquisition circuity configured for energy savings, which is highly important in implant-wearable devices, such as wearable data acquisition and wireless transmission module <NUM>.

<FIG> is a block diagram of a multi-channel rakeness data acquisition circuitry <NUM> for use with an analog acquisition front end that employs a single analog-to-digital convertor (ADC) <NUM>. In one exemplary embodiment, acquisition circuitry <NUM> is comprised in data acquisition module <NUM> of system <NUM> of <FIG>. In another exemplary embodiment, acquisition circuitry <NUM> is comprised in wearable data acquisition and wireless transmission module <NUM> of <FIG>.

In <FIG>, each of the L electrograms X<NUM> X<NUM>,. XL (acquired by electrodes <NUM>, <NUM>,. L) is preprocessed in respective front-end circuitries 701_1, 701_2,. 701_L, by multiplying the electrogram with a pseudo-random code, comprising a sequence in time of "<NUM>", "<NUM>", and "-<NUM>" using a low-cross-correlation (LCC) PRBS generator <NUM> to generate the "<NUM>", "<NUM>", and "-<NUM>" signals (e.g., sequences) having low cross-correlation.

Alternatively (<NUM>), a Walsh-Hadamard orthogonal coding can be applied to the analog signals, by using instead of LCC-PRBS generator <NUM>, an LCC Walsh-Hadamard orthogonal coding (LCC WHOC) generator <NUM>. Using generator <NUM> ensures very low cross-correlation between the channels and also suppresses <NUM>/f noise and offset.

The rakeness-processed (e.g., rakeness-coded) electrograms are first summed by an adder <NUM> and only then inputted into a single analog-to-digital convertor (ADC) <NUM>, thereby saving one energy-costly ADC element per channel (i.e., reducing the number of ADC elements from L>><NUM> to one).

A recording algorithm <NUM>, such as may be used by processor <NUM> of system <NUM>, or by signal reconstruction unit <NUM> of base station <NUM> of <FIG>, recovers the compressed sensing signal.

Signal reconstruction unit <NUM> can perform the reconstruction of the pseudorandom codes that are different per channel. While having the same energy spectrum and the same length, each pseudorandom code (e.g., fPBRSj) modulates a respective channel signal (e.g., Xj) by a different sequence of <NUM>, -<NUM> and <NUM>. Using the known sensing matrix Φ, the basis in which the signal is sparse, Ψ, and the measurements "y(t)" (i.e., the output signals in <FIG>), a processor estimates the aforementioned vector α. With α estimated the processor can reconstruct the original vector signal "x(t)" (i.e., the input analog signals in <FIG>).

The circuitry shown in <FIG> is shown in a simplified manner, for clarity of presentation. Possible implementation details, such as given in <FIG>, are thus omitted from <FIG>.

<FIG> are block diagrams of data acquisition circuitries <NUM> and <NUM> using rakeness to suppress <NUM>/f noise and offset, and compressed sensing (<FIG> only).

<FIG> shows circuity <NUM> used in <FIG>, in which a low noise amplifier (LNA) <NUM> is preceded by a modulator to suppress the amplifier's <NUM>/f noise and offset contribution. The technique used herein is spreadspectrum modulation. Since the input signal is spread over a larger bandwidth, the transmission is more secure and is also protected from interfering signals (e.g., <NUM>/<NUM>). At the output of LNA <NUM>, the signals are demodulated using the same PRBS sequence to obtain the amplified input signal.

<FIG> shows circuitry <NUM> used in <FIG>, in which a modulator is preceding a CS front-end to not only apply rakeness but also benefit from suppression of the integrating amplifier's <NUM><NUM>/f noise and offset.

Although the embodiments described herein mainly address compressed-sensing electrophysiological data, the methods and systems described herein can also be used in other applications, such as with CS of other forms of nonstationary data, such as originating from (bio-) sensors or in-vitro electrophysiological analysis, such as signals originating from cellular or molecular level (e.g., from a cell culture).

Claim 1:
An apparatus (<NUM>), comprising:
data acquisition circuitry (<NUM>) configured to acquire multiple signals using multiple respective electrodes of an array of electrodes (<NUM>) coupled to one of i) an organ of a patient and ii) tissue or cell culture; and
a processor (<NUM>), which is configured to:
hold a definition of a mixed-norm that is defined as a function of relative positions of the electrodes in the array; and
jointly compress the multiple signals in a compressed-sensing, CS, process that minimizes the mixed-norm,
characterized in that the data acquisition circuitry is further configured to apply a respective pseudo-random sequence to each of the signals so as to increase sparsity and incoherence of a measurement matrix Y based on the correlation between the respective signal and the respective pseudo-random sequence, and wherein the processor is configured to minimize the mixed-norm for the measurement matrix Y having the increased sparsity and incoherence.