In the process for mapping structural entity 222, receiving, by transmitters 218, time-varying voltage signals 216 from primary electromagnetic wave synthesizers 214 includes producing voltage signals that are pseudo-random binary sequences having an amplitude from a few mV to hundreds of V peak-to-peak with each voltage transition rise and fall edges in a time from 10 ps and 1 ns and each voltage level corresponding to a binary number, 1 or 0, in a time from 100 ps to several ns.

In the process for mapping structural entity 222, synchronously transmitting, by transmitters 218, time-varying voltage signals 216 as primary electromagnetic waves 220 includes producing wave disturbances that propagate in free space and mimic voltage signals that are pseudo-random binary sequences having an amplitude from a few mV to hundreds of V peak-to-peak with each voltage transition rise and fall edges in a time from 10 ps and 1 ns and each voltage level corresponding to a binary number, 1 or 0, in a time from 100 ps to several ns.

In the process for mapping structural entity 222, subjecting primary electromagnetic waves 220 to scattering by structural entity 222 includes the transmission, reflection, deflection, refraction and other forms of scattering of electromagnetic waves by media other than free space.

In the process for mapping structural entity 222, producing scattered electromagnetic waves 224 from primary electromagnetic waves 220 in response to scattering primary electromagnetic waves 220 by structural entity 222 includes producing a wave by interaction of incident electromagnetic waves 220 with the structural entity.

In the process for mapping structural entity 222, receiving, by receivers 226, scattered electromagnetic waves 224 includes detecting any wave communicated to the receiver after being scattered by the structural entity.

In the process for mapping structural entity 222, producing, by receivers 226, receiver signals 228 based on scattered electromagnetic waves 224 includes making a time varying signal that includes a linear combination of the transmitted signal modulated by the structural entity.

In the process for mapping structural entity 222, receiving, by conversion stage 230, receiver signals 228 from receivers 226 includes converting, by modules, analog signal 228 into a digital form that is processed by the render. An exemplary module is an analog-to-digital converter, a frontend amplifier, a mixer, filter, and the like.

In the process for mapping structural entity 222, receiving, by conversion stage 230, trigger voltage signal 212 from trigger voltage source 210 includes receiving voltage signals that pseudo-random binary sequences and having rise or fall edges from −1 V to 2.7 V in a time from 10 ps to 1 ns.

In the process for mapping structural entity 222, producing, by conversion stage 230, converted data 232 from receiver signals 228 and trigger voltage signal 212 includes producing numerical representations of analog signal 228 in a digital form such as 8-bit, 16-bit, 32-bit, or 64-bit integer or floating-point.

In the process for mapping structural entity 222, receiving, by render 234, converted data 232 from conversion stage 230 includes a program stored in hardware such as a field-programmable gate array (FPGA) or in a digital computer. The program contains a recovery algorithm that uses the digital signal 232 and creates a digital representation of the structural entity 236. The algorithm can use a variety of recovery techniques based on least squares (L2 minimization) or compressed sensing (L1 minimization).

In the process for mapping structural entity 222, producing map 236 of structural entity 222 from converted data 232 includes producing a 2D or 3D image to be displayed in, e.g., a digital monitor.

The process for mapping structural entity 222 also can use other computational means for the recovery algorithm in 234 such as graphics processing units (GPUs). Trigger voltage signal can be sent via coaxial cable or wirelessly via any synchronization protocol used for example in clock recovery. Transmitter 218 and receiver 228 can be mounted on mechanically rigid structures such as fire trucks or in a dynamically configurable system such as a drone.

Mapping probe 200 and processes disclosed herein have numerous beneficial uses, including fast response times (e.g., in microseconds) for real-time monitoring of movements; mapping 1D, 2D and 3D structural entities such as tunnels, individual floors, or whole buildings; tagging structural features based on recovered image contrast; using mapping probe as a metrology tool in identification and characterization of different materials; accommodating sizes of structural entities from a few centimeters to thousands of kilometers. Advantageously, mapping probe 200 overcomes limitations of technical deficiencies of conventional articles such as multiple reflection signals (multipath), long image recovery times, and dependence on prior knowledge of the structural entity. Further, this process allows for dynamic deployment in unknown scenarios and provides timely answers for mission critical activities such as search and rescue in a burning building.

Moreover, mapping probe 200 and processes herein have numerous advantageous properties. In an aspect, providing image recovery with the mapping probe can be provided via cloud service access, remote sensing, and the like.

Mapping probe 200 and processes herein unexpectedly involve small bandwidths for sensing with as few as one receiver 228 transmitting at data rates compatible with voice channels that overcomes technical limitations involved with more bandwidth intensive means such as live video feeds. Moreover, the mapping probe provides refresh rates of tens to hundreds of milliseconds for real-time updates.

Example

Real Time Signal Sampling and Recovery Using Engineered Electromagnetic Interference with a Mapping Probe.

A superposition, also referred to herein as interference, of propagating electromagnetic waves is generated by a set of transmitters to sample signals in real time. A signal can be a structural entity in a propagation medium that scatters electromagnetic waves. Data y, measured by detectors, corresponds to an inner product of a dynamically-generated interference-based sampling matrix A and signal x. Sampling occurs at a propagation speed of the waves, i.e., in real time. The signal can be sparse so that recovery occurs by aggregation and can include computational optimization, e.g., with compressive sensing.

Naturally occurring signals can be sparse so that they carry little information as provided for in compression used in digital cameras that operate in a visible band of the electromagnetic spectrum. Even though signal sparsity exists in other bands, detection thereof can be difficult and expensive. Non-invasive imaging provides sparse data, wherein a three-dimensional medium can be characterized by a small number of parameters in addition to embedded lower dimensional interfaces. Sampling of such media occurs with penetrating radiation such as radiofrequency (RF) waves, acoustic waves, infrared radiation, or x-rays. Detection at such wavelengths is difficult with a large array.

Compressed sensing is a signal recovery algorithm and technique that exploits a sparsity and inherent reciprocity between illumination and detection to make imaging in forbidden bands of the spectrum accessible. In signal analysis, a matrix A∈R^M×Nsamples signal x∈R^Nand retain sampling inner products in a measurement vector y∈R^M, i.e.,

Ax=y. (1)

To recover x, provided M≥N, take a pseudo inverse of A and multiply it by y. This procedure becomes impractical if N is very large as in the case of discretized two- and three-dimensional spaces. If M<N, the inversion problem is ill-posed and is intractable in general. However, if x is compressible or sparse, then recovery can be achieved by computational imaging and further optimized by compressed sensing methods with a small number of measurements M such that K<M<<N, wherein K is a number of non-zero components of x in a suitable basis such as discrete cosines or wavelets where most signals of interest are compressible or sparse. To ensure recovery with a small number of measurements M c K log (N/K), a strategy is to have the sampling matrix A contain incoherent random entries following, e.g., a Gaussian or Bernoulli distribution. Computational imaging methods recover x by simple aggregation {circumflex over (x)}=y^TA^T, whereas compressed sensing methods search for x by minimizing ∥z∥_P, subject to A z=y, wherein ∥z∥_p, (0<p≤1) is an [Image Omitted] _pnorm.

These methods involve compression at a sampling stage instead of a conventional approach to compression where the signal is sampled at full resolution by an array of detectors and subsequently compressed. This new method provides a measurement apparatus to have as few as a single detector while the illumination source retains full resolution with the corresponding computational load transferred to the recovery stage. The reversal of roles between sources and detectors overcome limitations in regions of the electromagnetic spectrum where the cost of high pixel count sensor arrays is prohibitive. It reciprocally transfers a burden of spatial resolution to the illumination system that now generates structured sampling patterns at full resolution. Furthermore, regardless of three-dimensional imaging recovery schemes at optical wavelengths, radar at radio frequencies, and ultrasound, improvements in real-time penetrating spatial reconstruction is provided by the mapping probe herein. Conventional devices involve sampling that has static patterns and lack full three-dimensional coverage.

The mapping probe, e.g., shown in FIG. 2, provides full-space three-dimensional sampling at the speed of the propagating waves in the medium by manipulating interference effects during propagation and compression of the sampling patterns that reduces a number of transmitters in the illumination system.

The mapping probe includes N_ttransmitters and N_rreceivers placed in the space where the signal is embedded, and the ensemble of transmitters, receivers, and signal are referred to as a scene. An arrangement of transmitters and receivers is arbitrary. Selection of a location occurs and provides for knowing their location; synchronizing, by a master clock, a transmission and reception process; and knowing the excitation waveforms on each transmitter.

Each transmitter independently has a waveform source connected to an antenna by a coaxial cable. The source has limited bandwidth and typically contains an oscillator connected to a quadrature-amplitude modulation stage such as an I-Q mixer. Synchronization ensures that the excitation waveforms exit the transmitters simultaneously with the start of data acquisition by the receivers.

The waveforms are tailored to produce modulations in the form of, amplitude modulation, frequency modulation, polarization modulation, or phase modulation.

Each receiver has an antenna connected to a demodulation stage, such as an I-Q mixer, by a coaxial cable. The mixer output is then digitized and stored for the recovery step.

A sampling matrix A according to Eqn. (1) is obtained and based on a model of point sources as the illumination system, a spatially dependent reflectivity function as the signal and small number of detectors. With regard to recovery of signals, to construct A in (1), a random intensity pattern is created by interference between fields formed by an array of N_Ttransmitters driven by Dirac pulses. The pulses are amplitude modulated by pseudo-random codes of polarity ±1. We thus model each transmitter (T_j, j=1 . . . N_T) as point sources placed in space-time at (r_j″, t_j″) polarized along the same direction a. The total illumination function is thus given by E=E_j∝E_j, where:

E
j

(

r
′

,

t
′

)

=

∑
k

C
jk

(

t
k
″

)

⁢

δ
[

c
⁡
(

t
′

-

t
k
″

)

-

❘
"[LeftBracketingBar]"

r
′

-

r
j
″

❘
"[RightBracketingBar]"

]

❘
"[LeftBracketingBar]"

r
′

-

r
j
″

❘
"[RightBracketingBar]"