**2. Coarray: New paradigm for the design of imaging systems**

2 Breakthroughs in Ultrasound Imaging

real-time ultrasonic image.

the following aspects:

velocity [6].

imaging [7].

and future research developments.

3. **Medium penetration**. And for the same reason, the penetration deep of ultrasound in the region of interest is smaller than the achieved using conventional imaging techniques

In order to reduce some of these drawbacks, more sophisticated SAFT techniques have been proposed. Total Focusing Method (TFM) [1] is one of them, where each array element is sequentially used as a single emitter and all array elements are used as receivers. Thus, it is possible to obtain a set of *N* × *N* signals (Full Matrix Array capture, FMA) that is used to form the image. According to the description of professors Drinkwater and Wilcox [1–3], its name refers to the possibility of implementing dynamic focusing in emission and reception, which enables to obtain images perfectly focused at all points in the region of interest. However, the complexity of the acquisition process and the computational requirements of the beamforming make this method not appropriate for real-time purposes [1]. Other solutions that use an emission and reception sub-aperture have been also proposed [4–6], although they maintain a certain degree of hardware complexity (focussing is needed in emission and reception) and also require intensive computational capabilities to produce a

To overcome the last inconveniences we propose a SAFT methodology based on a new paradigm, known as coarray [5, 6], which allows to use only one element in emission and a limited number of parallel channels in reception at each time. With the proposed solution, a strategy for a hardware reduction in ultrasonic imaging systems is possible, and it involves

• Optimization of the acquisition strategies to achieve the completeness of the coarray with a minimum number of hardware elements. In this sense, our objective is to establish a trade-off between the number of electronic channels, image quality and acquisition

• The use of pulse compression techniques to overcome the reduced capability of

• The development of GPGPU1 parallel beamforming techniques to achieve real time

This chapter is divided into two main sections. The first one is dedicated to analyse the use of the coarray paradigm as a tool for the design of ultrasonic imaging systems and to present several minimum redundancy coarray techniques. Moreover, Golay codes are presented and their integration within the presented SAFT methods is described. The second section presents the general ultrasonic imaging system's overview, its architecture and the parallel beamforming as a solution for ultrafast beamforming. Finally, we expose our conclusions

<sup>1</sup> General-purpose computing on Graphics Processing Units is the utilization of a graphics processing unit (GPU), which typically handles computation only for computer graphics, to perform computation in applications

penetration when emission is limited to one element [5].

traditionally handled by the central processing unit (CPU). http://gpgpu.org

(e.g. needed by cardiac imaging or industrial inspections).

This section is focused on the development of ultrasonic imaging systems based on the pulse/echo aperture model which is known as coarray. In order to clarify this point, we are going to briefly review this mathematical concept and its principal implications.

The coarray is a mathematical tool that is often used by several authors as a way to quickly study the radiation properties of an imaging system [5, 6, 8, 9]. This concept is frequently referred to as *effective aperture* in ultrasound literature, and it basically is the virtual aperture which produces in one way the same beam pattern as the real aperture working in emission and reception as Figure 12 suggests.

Suppose a linear array with *N* elements. In far-field and assuming very narrow band signals, the radiation pattern could be written as:

$$f(u) = \sum\_{n=0}^{N-1} a\_{n} e^{jkx\_{n}u} = \sum\_{n=0}^{N-1} a\_{n} e^{jkndu} = \sum\_{n=0}^{N-1} a\_{n} (e^{jkdu})^{n} \tag{1}$$

where *an* are the complex weights of the transducers and *u* = *sin*(*θ*) being *θ* the angle measured from the perpendicular to the array. Substituting *ejkdu* by the complex variable *z*, the radiation pattern can be expressed as a polynomial, which corresponds with the Z-Transform of the sequence *an*. Thus, considering a pulse-echo system, the complex radiation pattern will be the product of two polynomials with degree *N* − 1:

$$f\_{\text{total}}(z) = Z\{c\_n\} = \sum\_{n=0}^{2N-2} c\_n z^n = \sum\_{n=0}^{N-1} a\_n z^n \cdot \sum\_{n=0}^{N-1} b\_n z^n \tag{2}$$

where *an* and *bn* are the gains applied to the transducers in emission and reception, and *cn* is the coarray (*Z*{*cn*} represents the Z-Transform of the sequence *cn*). Returning to the unit circle (|*z*| = 1 , *z* = *ejkdu*) and considering equation 1 then the radiation pattern of the system in continuous wave is directly the DFT of the coarray [10].

In synthetic aperture systems, each scanned image is obtained after several firing sequences of the elements. According to this, the coarray can then be expressed as a sum of several sub-coarrays. Each of these sub-coarrays will be obtained as the convolution of two sub-apertures that represent the weights of the active elements used to emit and receive the signals each time.

Figure 1 illustrates the coarray generated by TFM method, which has been applied in ultrasound area since the late 60's and early 70's [11, 12]. As we briefly introduced in Section 1, it consists on the sequential emission with each one of the array elements in turn, and the reception in each shot with the full transducer aperture. As we can see, its coarray is fully populated what ensures a grating-lobe free radiation pattern.

The image quality achieved when TFM is employed is the highest possible, but it has, as its counterpart, the huge volume of data which is necessary to acquire. Thus, it requires more storage resources and processing capability than other techniques, which makes difficult its

acquisition velocity maintaining the highest quality and producing high frame rates with low

Strategies for Hardware Reduction on the Design of Portable Ultrasound Imaging Systems

http://dx.doi.org/10.5772/55910

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Coarray analysis identifies which emitter-receiver combination completes each of its elements. In the TFM method seen before, we find that some of the elements are formed by a single signal (in concrete boundary elements) while the others increase progressively until reaching coarray centre with a value of *N* elements (Figure 1). Thus, we can consider as a minimum redundancy coarray that in which each element is composed of only one signal. Therefore, using the minimum possible number of signals the aperture's diffraction properties can be improved by manipulating the gain of the elements. With this goal in mind, it is possible to establish several strategies which maintain a balance between the number of

2R-SAFT technique [14] has some particular advantages that make it very useful for ultrasonic imaging systems. 2R-SAFT uses only one element to transmit and two elements to receive. As it is shown in Figure 2, all elements are consecutively activated as single emitters, without the use of any beamformer in emission. At each shot, two consecutive channels are

*th* element is used to emit a waveform, *i* and *i* + 1 elements are used for

receiving signals. For the last element of the array, only one signal is recorded. By employing an emitter in each shot all the received signals are completely uncorrelated, containing only

Figure 3 shows the coarray generated when 2R-SAFT is employed. As we can observe, the coarray is fully populated ensuring the suppression of grating lobes in the radiation pattern

Here we present a minimum-redundancy technique we have denominated Accelerated-SAFT or, in its short form, kA-SAFT. The k subscript refers to the acceleration factor carried out during the acquisition stage which can go from 2x to Nx depending on the number of

power consumption. This topic will be the main focus of next two sections.

parallel channels and the number of shots during acquisition processes.

used as receivers requiring to store two signals per emission.

**2.1. Minimum redundancy coarray solutions**

*2.1.1. 2R-SAFT acquisition strategy*

**Figure 2.** Firing sequences of the elements in 2R-SAFT

information of a single transmitter-receiver pair.

which produces good quality images [14, 15].

*2.1.2. Accelerated-SAFT acquisition strategy*

Thus, when the *i*

**Figure 1.** Firing sequences of the elements in TFM, and its corresponding generated coarray

practical implementation with todays' technology. To illustrate this, consider the following example: a 15 cm depth image, 40 MHz sampling rate, 64 channels, 1500 m/s medium velocity and 2 bytes per sample. Each firing generates approximately 1 MB of pulse-echo data, what supposes 64 MB of data to generate a single image frame when TFM is applied. For a frame rate of 20 images per second, it would be necessary to acquire and process 1.2 Gbytes of data per second.

The bandwidth of most I/O standards available today put in evidence that any of current data protocols can not deal with TFM requirements. Supposing a good efficiency and use of the resources (around 80)%, USB 2.0 port (released in April 2000) would be able to transfer less than one image per second (48 MB/s). A similar situation occurs if USB 3.0 (released in November 2008) is employed, being the maximum transmission speed up to 480 MB/s allowing to transfer around 7 images per second, even far respect to the maximum number of images which could be theoretically achieved. Finally, the most recent standard released in February 2011, known as Thunderbolt port and developed by Intel [13], combines PCI Express and DisplayPort into a new serial data interface that can be carried over longer and less costly cables. Thunderbolt has twice the transfer speed of USB 3.0 over copper wire (960 MB/s) giving us transferences of 14 images per second.

Therefore, it is clear that a reduction of data volume is desirable. In this sense, applying the coarray concept permits us to propose system designs that use less channels simultaneously working in emission and reception, but maintaining the same level of image quality. The key point for this is to use the coarray to search for solutions of minimum redundancy. This approach in conjunction with parallel computing techniques will offer an increment of acquisition velocity maintaining the highest quality and producing high frame rates with low power consumption. This topic will be the main focus of next two sections.
