Research ArticleAPPLIED SCIENCES AND ENGINEERING

Compressive 3D ultrasound imaging using a single sensor

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Science Advances  08 Dec 2017:
Vol. 3, no. 12, e1701423
DOI: 10.1126/sciadv.1701423
  • Fig. 1 The three techniques of ultrasound imaging formation.

    Conventional ultrasound imaging requires an array of sensors to (A) focus the transmitted and received wave field or (B) only the received wave field by postprocessing the individual signals after analog-to-digital conversion (ADC). We propose using only one sensor without focusing in transmission or receive (C).

  • Fig. 2 A spatiotemporally varying ultrasound field allows for compressive imaging.

    (A) One sensor (transmitter and receiver) cannot distinguish between two objects when the transmitted wave field has no spatiotemporal diversity. (B) A simple coding mask can introduce a spatiotemporally varying wave field, which allows unique signal separation between two objects.

  • Fig. 3 A random delay coding mask breaks the phase uniformity of the ultrasound transmission to enable compressive imaging.

    The top panel shows the ultrasound field transmitted from a normal piezoelectric sensor recorded by a small microphone (hydrophone) in front of the sensor. Note that the transmitted wave focuses naturally into a narrower bundle after propagation. The bottom panel shows the same transmitted wave field after propagation through the plastic coding mask. Here, the phase uniformity of the wave is completely lost. The images in (A) and (D) show one time sample (at 8.75 μs) of the transmitted wave field in a 2D plane (12.7 mm away from the sensor surface) perpendicular to the propagation axis, before and after the addition of the coding mask. The images in (B) and (E) show a projection of the total ultrasound energy over time in the same 2D plane that is used for (A) and (D). The images (C) and (F) show the energy projection over time in a 2D plane parallel to the ultrasound propagation axis.

  • Fig. 4 Spatiotemporal diversity as well as wave field rotation provides a unique signal for every pixel.

    (A) A 2D slice (time and y dimension) of the 4D ultrasound field (time and three spatial dimensions), where x = 0 and z = 12.7 mm. Every time sample of this 4D wave field has unique spatial properties, as is shown in (B) and (C). (B) The spatial ultrasound field at a later point in time contains higher spatial frequencies, which is desirable for reconstructing objects with high resolution. The possibility of rotating the mask offers another dimension of signal variation to be used for image reconstruction. (C) Analysis of two samples based on their spatial properties with respect to coding mask rotation. For pixels further away from the center, the local variance is higher than for pixels closer to the center.

  • Fig. 5 Random delays in the coding mask generate signal variability for unique pixel reconstruction.

    (A) Schematic drawing of the approximated ultrasound field in a plane inside the medium parallel to the sensor surface. For every pixel in this plane, we want the echo signals to be as uncorrelated/orthogonal as possible. (B) The histograms show the cross-correlation values of a large set of pixels in the plane, obtained using an approximate simulation model. When the plastic delay mask is rotated, the cross-correlation values distribute closer to zero, which suggests better image reconstruction. (C) Mask layout where the gray values indicate the thickness variations, causing local delays of the ultrasound field. (D) Local correlations for a pixel at a fixed (x, y) position at several depths using 72 mask rotations. (E) CRLB analysis. The leftmost panel shows the level curves for one SD of position estimation error for a depth z of 12.7 mm. The center graphs show the SD in x, y, and z over radius (distance to the center of rotation) at depth 12.7 mm, and over depth for a pixel at a distance of 3 mm from the center. The rightmost graph shows how the CRLB changes as more measurements are added by rotation for a pixel at a distance of 3 mm from the center and at a depth of 12.7 mm.

  • Fig. 6 Compressive 3D ultrasound imaging using a single sensor.

    (A) Schematic sketch of the signal model involved in this type of compressive imaging. Each column of the observation matrix H contains the ultrasound pulse-echo signal that is associated with a pixel in 3D space, which is contained in the image vector v. By rotating the coding mask in front of the sensor, we obtain new measurements that can be stacked as additional entries in the measurement vector u and additional rows in H. (B) Result of solving part of the image vector v using an iterative least squares technique. The two images are mean projections of six pixels along the z dimension [individual z slices shown in (D)]. (C) Schematic overview of the complete imaging setup. A single sensor transmits a phase uniform ultrasound wave through a coding mask that enables the object information (two plastic letters “E” and “D”) to be compressed to a single measurement. Rotation of the mask enables additional measurements of the same object. (D) Reconstruction of the letter “E” in six adjacent z slices. A small tilt of the letter (from top left corner to bottom right corner) can be observed, demonstrating the potential 3D imaging capabilities of the proposed device. (E) Image showing the two 3D-printed letters and the plastic coding mask with a rubber band for rotating the mask over the sensor. The two right-hand panels show close-ups of the plastic coding mask. (F) 3D rendering of the complete reconstructed image vector v, obtained by BPDN. The images shown in (B) and (D) were obtained using 72 evenly spaced mask rotations, and the full 3D image in (F) was obtained using only 50 evenly spaced rotations to reduce the total matrix size.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/12/e1701423/DC1

    text S1. On the size of the system matrix H.

    text S2. Comparison with multisensor array imaging.

    text S3. On the relation to CS.

    fig. S1. Imaging performance for a single sensor with coding mask and normal sensor arrays without coding mask.

    fig. S2. Image reconstruction example for a sensor array and a single sensor with coding mask for a comparable amount of measurements.

    movie S1. A random delay coding mask breaks the phase uniformity of the ultrasound transmission to enable compressive imaging.

    movie S2. Compressive 3D ultrasound imaging using a single sensor.

    movie S3. Image reconstruction for a multisensor array and a single sensor with rotating coding mask.

    Reference (43)

  • Supplementary Materials

    This PDF file includes:

    • text S1. On the size of the system matrix H.
    • text S2. Comparison with multisensor array imaging.
    • text S3. On the relation to CS.
    • fig. S1. Imaging performance for a single sensor with coding mask and normal sensor arrays without coding mask.
    • fig. S2. Image reconstruction example for a sensor array and a single sensor with coding mask for a comparable amount of measurements.
    • Legends for movies S1 to S3
    • Reference (43)

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1(.mp4 format). A random delay coding mask breaks the phase uniformity of the ultrasound transmission to enable compressive imaging.
    • movie S2 (.mp4 format). Compressive 3D ultrasound imaging using a single sensor.
    • movie S3 (.mp4 format). Image reconstruction for a multisensor array and a single sensor with rotating coding mask.

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