# US 2020/0400802 A1 · Reconstruction system and method

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- Number: US 2020/0400802 A1
- Document ID: US20200400802A1
- Status: Published application
- Kind: A1
- Application number: 16/975,105
- Filed: 2019-02-25
- Published: 2020-12-24
- Earliest claimed: 2018-02-23
- Assignees: Carpatchiot B.V.
- Applicants: Carpatchiot B.V.
- Inventors: Miaomiao ZHANG
- Web page: https://patentgrep.com/patent/US20200400802A1

## CPC

- G01S 7/52034: {Data rate converters}
- G01S 7/52028: {using digital techniques}
- G01S 7/52046: {Techniques for image enhancement involving transmitter or receiver (image enhancement by image data processing G06T5/00)}
- G01S 7/52087: {using synchronization techniques (control of medical diagnostic ultrasound devices involving acquisition triggered by a physiological signal A61B8/543)}
- G01S 7/52092: {using frequency diversity}
- G01S 15/8915: {using a transducer array}
- G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES

## Abstract

A method for reconstructing a signal from a subset of the full signal is disclosed. In one embodiment, the method includes receiving a plurality of randomly sampled multichannel radio-frequency or in-phase and quadrature signals acquired from a physical environment including a transmitter, a propagation medium and a receiver; modelling the full signal as a matrix comprising a plurality of vector signals, wherein the full signal is expressed as a matrix product of a first matrix and a second matrix; updating the second matrix based on an objective function to produce an updated second matrix; determining a convergence parameter in dependence upon the evaluated objective function; and modifying the updated second matrix in dependence upon the convergence parameter.

## Claims

### Claim 1

A method for estimating a full signal X from a subset B of the full signal X, the method comprising: receiving a plurality of randomly sampled multichannel radio-frequency or in-phase and quadrature signals acquired from a physical environment comprising a transmitter, the transmitter comprising one or more transmitting elements for emitting ultrasound excitation pressure waves, a propagation medium containing non-uniformities capable of reflecting said excitation pressure waves, and a receiver for receiving the full signal X, wherein the receiver comprises one or more receiver elements;
modelling the full signal X as a matrix comprising a plurality of vector signals, each vector signal corresponding to the full signal X incident on a corresponding receiver element, wherein each vector signal comprises a plurality of samples representing the full signal X sampled from a corresponding receiver element, wherein each sample comprises a weighted sum of complex sinusoids, wherein the full signal X is expressed as a matrix product of a first matrix Y and a second matrix D;
updating the second matrix D based on an objective function, wherein the objective function is configured to estimate the second matrix D based on the plurality of randomly sampled signals, to produce an updated second matrix Dl;
determining a convergence parameter in dependence upon the evaluated objective function; and
modifying the updated second matrix Dl in dependence upon the convergence parameter.

### Claim 2 (depends on 1)

The method according to claim 1, wherein modifying the updated second matrix Dl in dependence upon the convergence parameter comprises comparing the convergence parameter with a predetermined threshold value.

### Claim 3 (depends on 2)

The method according to claim 2, further comprising, if the convergence parameter is greater than the predetermined threshold value, repeating the step of evaluating the objective function for a modified first trial matrix.

### Claim 4 (depends on 2)

The method according to claim 2, further comprising, if the convergence parameter is less than the predetermined threshold value, determining an estimated full signal X in dependence upon the updated second matrix Dl and the first matrix Y.

### Claim 5 (depends on 4)

The method according to claim 4, further comprising outputting the estimated full signal X.

### Claim 6 (depends on 1)

The method according to claim 1, wherein the complex sinusoids have a finite number k of distinct frequencies.

### Claim 7 (depends on 6)

The method according to claim 6, wherein each weighted sum comprises sinusoids at the same k distinct frequencies.

### Claim 8 (depends on 7)

The method according to claim 7, wherein the second matrix Y comprises the set of k complex sinusoids.

### Claim 9 (depends on 8)

The method according to claim 8, wherein the second matrix D comprises, for each vector signal, a set of k coefficients corresponding to the complex sinusoids.

### Claim 10 (depends on 9)

The method according to claim 9, wherein a rank of the first matrix X is less than k.

### Claim 11 (depends on 1)

The method according to claim 1, wherein the transmitter is configured to emit ultrasound excitation pressure waves having frequencies within a frequency band.

### Claim 12 (depends on 11)

The method according to claim 11, wherein the complex sinusoids have frequencies within the frequency band.

### Claim 13 (depends on 1)

The method according to claim 1, wherein estimating the full signal X comprises a simultaneous direction method of multipliers method.

### Claim 14 (depends on 4)

The method according to claim 4, wherein estimating the full signal X comprises a minimizing process of a nuclear norm of the full signal X.

### Claim 15 (depends on 1)

The method according to claim 1, wherein estimating the full signal X comprises a minimizing process of an I norm of the second matrix D.

### Claim 16 (depends on 4)

The method according to claim 4, further comprising generating an image in dependence upon the estimated full signal X.

### Claim 17

(canceled)

### Claim 18

(canceled)

### Claim 19

(canceled)

### Claim 20

An apparatus for performing ultrasound measurements of a propagation medium containing non-uniformities, the apparatus comprising:
an ultrasound transducer configured to emit ultrasound excitation pressure waves;
a receiver comprising one or more elements for receiving a full signal X resulting from reflection of said excitation pressure waves by the non-uniformities; and
a processor configured to receive a set of random samples B of the full signal X or of a demodulated full signal X and to estimate the full signal X from the set of random samples, wherein the processor is configured to perform the steps of:
modelling the full signal X as a matrix comprising a plurality of vector signals, each vector signal corresponding to the full signal incident on a corresponding receiver element, wherein each vector signal comprises a plurality of samples representing the full signal sampled from a corresponding receiver element, wherein each sample comprises a weighted sum of complex sinusoids, wherein the full signal X is expressed as a matrix product of a first matrix Y and a second matrix D;
updating the second matrix D based on an objective function, wherein the objective function is configured to estimate the second matrix D based on the randomly sampled signals, to produce an updated second matrix Dl;
determining a convergence parameter in dependence upon the evaluated objective function; and
modifying the updated second matrix Dl in dependence upon the convergence parameter.

### Claim 21 (depends on 19)

The apparatus according to claim 19, further comprising a sampling element configured to receive the full signal X or a demodulated full signal X and to provide a set of random samples of the full signal B or of a demodulated full signal B to the processor.

### Claim 22

(canceled)

### Claim 23 (depends on 20)

The apparatus according to claim 20, wherein modifying the updated second matrix Dl in dependence upon the convergence parameter comprises comparing the convergence parameter with a predetermined threshold value.

### Claim 24 (depends on 23)

The apparatus according to claim 23, wherein the processor is configured to, if the convergence parameter is greater than the predetermined threshold value, repeat the step of evaluating the objective function for the updated second trial matrix.

### Claim 25 (depends on 23)

The apparatus according to claim 23, wherein the processor is configured to, if the convergence parameter is less than the predetermined threshold value, determine an estimated full signal X in dependence upon the updated second matrix Dl and the first matrix Y.

### Claim 26 (depends on 25)

The apparatus according to claim 25, wherein the processor is configured to output the estimated full signal X.

### Claim 27 (depends on 25)

The apparatus according to claim 25, wherein the processor is configured to generate an image in dependence upon the estimated full signal X.

### Claim 28

(canceled)