**2.1. Minimum redundancy coarray solutions**

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 parallel channels and the number of shots during acquisition processes.

## *2.1.1. 2R-SAFT acquisition strategy*

4 Breakthroughs in Ultrasound Imaging

Gbytes of data per second.

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

MB/s) giving us transferences of 14 images per second.

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

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

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 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 used as receivers requiring to store two signals per emission.

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

Thus, when the *i 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 information of a single transmitter-receiver pair.

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 which produces good quality images [14, 15].

#### *2.1.2. Accelerated-SAFT acquisition strategy*

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

*Elementsrx* =

**Figure 5.** Coarray sequences for kA-SAFT being k = 2x and *nA* = 4

images have been calculated using 2*N* − 1 = 127 signals.

relies fundamentally on the hardware requisites.

*2.1.3. Experimental results*

 *<sup>i</sup>* <sup>−</sup> *nA* <sup>2</sup> <sup>+</sup> *<sup>j</sup>* 

all its advantages but multiplying by 4 the frame rate in acquisition.

Figure 5 shows the coarray generated when kA-SAFT is employed for the case of *nA* = 4. As we can observe, the coarray is identical to that obtained with 2R-SAFT (Figure 3) preserving

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

We present some experimental results that have been done on a tissue phantom (Model 040GSE - CIRS Inc.) with 0.5dB/cm attenuation, where several cysts and wires of 0.1mm diameter are located at different depths (Figure 6). We have used a 2.6MHz phased array transducer with *N* = 64 elements, 0.28mm of pitch (Vermon Inc.) for the measurements. We will use the Total Focusing Method as a reference model to examine the cysts and wires in the tissue covering an area starting from 25mm to 80mm depth, and we will compare it to 2R-SAFT and kA-SAFT techniques. All images have been obtained by applying the DAS algorithm. TFM uses the complete set of signals *N*<sup>2</sup> = 4096 while 2R-SAFT and kA-SAFT

In Figure 7, images for all strategies are presented. It is easily observed how Figures 7(a,b,d,e,g) are very similar in terms of quality. Consequently, the strategy to be chosen

Nevertheless, at a depth greater than 60 mm none reaches the same contrast level as TFM (Figure 7(h)), highlighting the limited signal to noise ratio suffered by all minimum

<sup>0</sup> ≤ *<sup>j</sup>* ≤ *nA* (3)

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249

**Figure 3.** Coarray sequences for 2R-SAFT

channels used for the reception. This strategy increases a little bit the cost involved in the acquisition system respect to 2R-SAFT, but at the same time, reduces the number of shots by k times.

The kA-SAFT uses *nA* consecutive elements to receive and a single element to emit which is centred in the active subaperture. As shown in Figure 4, the elements on emission are sequentially activated with a shift of *nA* <sup>2</sup> elements. At each shot *nA* consecutive channels are used as receivers, needing to store *nA* signals per emission except for the first and the last array elements where half of the signals is acquired.

**Figure 4.** Firing sequences of the elements in kA-SAFT being k = 2x and *nA* = 4

In this sense, when the *i th* element is used to emit the elements that are going to use as receivers are given by:

$$\text{Elements}\_{rx} = \left\{ \mathbf{i} - \frac{\mathfrak{n}\_A}{2} + \mathbf{j} \right\} \qquad \qquad 0 \le \mathbf{j} \le \mathfrak{n}\_A \tag{3}$$

Figure 5 shows the coarray generated when kA-SAFT is employed for the case of *nA* = 4. As we can observe, the coarray is identical to that obtained with 2R-SAFT (Figure 3) preserving all its advantages but multiplying by 4 the frame rate in acquisition.

**Figure 5.** Coarray sequences for kA-SAFT being k = 2x and *nA* = 4

#### *2.1.3. Experimental results*

6 Breakthroughs in Ultrasound Imaging

**Figure 3.** Coarray sequences for 2R-SAFT

In this sense, when the *i*

receivers are given by:

sequentially activated with a shift of *nA*

array elements where half of the signals is acquired.

**Figure 4.** Firing sequences of the elements in kA-SAFT being k = 2x and *nA* = 4

k times.

channels used for the reception. This strategy increases a little bit the cost involved in the acquisition system respect to 2R-SAFT, but at the same time, reduces the number of shots by

The kA-SAFT uses *nA* consecutive elements to receive and a single element to emit which is centred in the active subaperture. As shown in Figure 4, the elements on emission are

used as receivers, needing to store *nA* signals per emission except for the first and the last

<sup>2</sup> elements. At each shot *nA* consecutive channels are

*th* element is used to emit the elements that are going to use as

We present some experimental results that have been done on a tissue phantom (Model 040GSE - CIRS Inc.) with 0.5dB/cm attenuation, where several cysts and wires of 0.1mm diameter are located at different depths (Figure 6). We have used a 2.6MHz phased array transducer with *N* = 64 elements, 0.28mm of pitch (Vermon Inc.) for the measurements. We will use the Total Focusing Method as a reference model to examine the cysts and wires in the tissue covering an area starting from 25mm to 80mm depth, and we will compare it to 2R-SAFT and kA-SAFT techniques. All images have been obtained by applying the DAS algorithm. TFM uses the complete set of signals *N*<sup>2</sup> = 4096 while 2R-SAFT and kA-SAFT images have been calculated using 2*N* − 1 = 127 signals.

In Figure 7, images for all strategies are presented. It is easily observed how Figures 7(a,b,d,e,g) are very similar in terms of quality. Consequently, the strategy to be chosen relies fundamentally on the hardware requisites.

Nevertheless, at a depth greater than 60 mm none reaches the same contrast level as TFM (Figure 7(h)), highlighting the limited signal to noise ratio suffered by all minimum 8 Breakthroughs in Ultrasound Imaging

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**Figure 7.** Experimental images from tissue phantom. (a) 2R-SAFT, (b) 2xA-SAFT, (c) Lateral profiles comparison between 2R-SAFT and 2xA-SAFT, (d) 4xA-SAFT, (e) 8xA-SAFT, (f) Lateral profiles comparison between 4xA-SAFT and 8xA-SAFT, (g)

The auto-correlation functions of *A*[*n*] and *B*[*n*] have side lobes with equal magnitude but opposite sign. The sum of these independent auto-correlation functions provides an ideal

> 

0, *n* = 0

2*N*, *otherwise*

(4)

*CA*[*n*] + *CB*[*n*] =

16xA-SAFT, (h) TFM, (i) Lateral profiles comparison between 16xA-SAFT and TFM

delta function according to:

**Figure 6.** Region of interest analysed from tissue phantom model 040GSE by CIRS Inc.

redundancy techniques. In table 1, a comparison between the number of channels in emission and reception, number of firings, acquisition frame rates and memory buffers needed is performed for the different strategies presented. As we can see, TFM is the technique which more storage as well as more hardware channels needs. By contrast, minimum redundancy techniques requisites are more affordable and suitable for applications where size matters.


**Table 1.** Comparison of the several acquisition strategies presented

#### **2.2. Golay Codes**

As we have seen, synthetic aperture images have low contrast due to the poor signal to noise ratio (SNR). Along this section, we will study how the use of pulse coding based on Golay codes [16, 17] can help to improve the dynamic range and SNR, in order to achieve an image quality comparable to that of Total Focusing Method.

#### *2.2.1. Golay encoding for ultrasonic excitation*

Golay complementary pairs have been widely used for transducer excitation because the sum of its auto-correlation function has a main peak and zero side-lobes [16]. A complementary pair is composed of two binary sequences, *A*[*n*]=[*a*0, *a*1,..., *aN*−1] and *<sup>B</sup>*[*n*]=[*b*0, *<sup>b</sup>*1,..., *bN*−1], of the same length *<sup>N</sup>* such that *ai*, *bi* ∈ {−1, +1}.

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8 Breakthroughs in Ultrasound Imaging

250 Advancements and Breakthroughs in Ultrasound Imaging

**Figure 6.** Region of interest analysed from tissue phantom model 040GSE by CIRS Inc.

2xA-SAFT (*nA* = 4) (1,4) *Nfirings* = *<sup>N</sup>*

8xA-SAFT (*nA* = 16) (1,16) *Nfirings* = *<sup>N</sup>*

16xA-SAFT (*nA* = 32) (1,32) *Nfirings* = *<sup>N</sup>*

**Table 1.** Comparison of the several acquisition strategies presented

quality comparable to that of Total Focusing Method.

*2.2.1. Golay encoding for ultrasonic excitation*

**2.2. Golay Codes**

redundancy techniques. In table 1, a comparison between the number of channels in emission and reception, number of firings, acquisition frame rates and memory buffers needed is performed for the different strategies presented. As we can see, TFM is the technique which more storage as well as more hardware channels needs. By contrast, minimum redundancy techniques requisites are more affordable and suitable for applications where size matters.

**Strategy Channels (tx,rx) Firings Framerate Buffer**

<sup>2</sup>*<sup>N</sup>* <sup>−</sup> <sup>1</sup> <sup>×</sup> *<sup>L</sup>* 4xA-SAFT (*nA* <sup>=</sup> 8) (1,8) *Nfirings* <sup>=</sup> *<sup>N</sup>*

As we have seen, synthetic aperture images have low contrast due to the poor signal to noise ratio (SNR). Along this section, we will study how the use of pulse coding based on Golay codes [16, 17] can help to improve the dynamic range and SNR, in order to achieve an image

Golay complementary pairs have been widely used for transducer excitation because the sum of its auto-correlation function has a main peak and zero side-lobes [16]. A complementary pair is composed of two binary sequences, *A*[*n*]=[*a*0, *a*1,..., *aN*−1] and *<sup>B</sup>*[*n*]=[*b*0, *<sup>b</sup>*1,..., *bN*−1], of the same length *<sup>N</sup>* such that *ai*, *bi* ∈ {−1, +1}.

*<sup>N</sup>* <sup>2</sup>*<sup>N</sup>* <sup>−</sup> <sup>1</sup> <sup>×</sup> *<sup>L</sup>*

*<sup>N</sup> <sup>N</sup>*<sup>2</sup> <sup>×</sup> *<sup>L</sup>*

<sup>2</sup> *<sup>f</sup> f rame* <sup>=</sup> <sup>2</sup> *fpr f*

<sup>4</sup> *<sup>f</sup> f rame* <sup>=</sup> <sup>4</sup> *fpr f*

<sup>8</sup> *<sup>f</sup> f rame* <sup>=</sup> <sup>8</sup> *fpr f*

<sup>16</sup> *<sup>f</sup> f rame* <sup>=</sup> <sup>16</sup> *fpr f*

*N*

*N*

*N*

*N*

2R-SAFT (1,2) *Nfirings* <sup>=</sup> *N f f rame* <sup>=</sup> *fpr f*

TFM (1,N) *Nfirings* <sup>=</sup> *N f f rame* <sup>=</sup> *fpr f*

**Figure 7.** Experimental images from tissue phantom. (a) 2R-SAFT, (b) 2xA-SAFT, (c) Lateral profiles comparison between 2R-SAFT and 2xA-SAFT, (d) 4xA-SAFT, (e) 8xA-SAFT, (f) Lateral profiles comparison between 4xA-SAFT and 8xA-SAFT, (g) 16xA-SAFT, (h) TFM, (i) Lateral profiles comparison between 16xA-SAFT and TFM

The auto-correlation functions of *A*[*n*] and *B*[*n*] have side lobes with equal magnitude but opposite sign. The sum of these independent auto-correlation functions provides an ideal delta function according to:

$$\mathbf{C}\_{A}[n] + \mathbf{C}\_{B}[n] = \begin{cases} \begin{array}{c} 0, n = 0 \\\\ 2N, otherwise \end{array} \end{cases} \tag{4}$$

10 Breakthroughs in Ultrasound Imaging

where *CA*[*n*] and *CB*[*n*] are the auto-correlation functions of *A*[*n*] and *B*[*n*], respectively, for any integer *n* satisfying the equation 4. The construction of Golay code pairs is done recursively with the *"negate and concatenate"* method, a technique used by Golay [16] to create longer pairs from shorter hand-constructed given pairs. Specifically, if *A*[*n*] and *B*[*n*] are the *N*-digit binary representations of a complementary pair of codes, then a new pair of complementary codes *<sup>A</sup>*′ [*n*] and *<sup>B</sup>*′ [*n*] of length 2*N* can be formed by concatenating *B*[*n*] to *A*[*n*] and concatenating ∼ *B*[*n*] to *A*[*n*] where ∼ *B*[*n*] is the complement of *B*[*n*]. Thus, *A*′ [*n*] = *<sup>A</sup>*[*n*] | *<sup>B</sup>*[*n*], and *<sup>B</sup>*′ [*n*] = *A*[*n*] |∼ *B*[*n*].

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1. The number of channels in reception (sensors) must double the original number, in order

2. The amount of acquired data signals also doubles the original, because of the first point. 3. The original firing rate is preserved, which means achieving identical performance at the

With the use of Golay codes to image the same area than in previous results, the panorama has changed. As before, TFM image has been composed from the complete set of signals *N*<sup>2</sup> = 4096, but now 2R-SAFT and kA-SAFT have been calculated using 4*N* − 2 = 254 signals. From Figure 7 in section 2.1.3, where the corresponding images with no encoding were analysed, it can be seen how the reduction in the number of signals employed produces a loss of dynamic range respect to TFM method. Thus, with the use of Golay codes in Figure 9 we can observe how the contrast and level of detection have substantially increased. Now, both 2R-SAFT and kA-SAFT techniques distinguish the complete set of defects. Thus, in relation to TFM the number of signals is drastically reduced from *N*<sup>2</sup> to 4*N* − 2, accelerating

As we have said, our goal is centred in the design of ultrasonic imaging systems based on solutions which require fewer resources and storage capacity than conventional systems. Thus, in Figure 10 is schematically represented our vision of the system, which is composed

1. **The array or probe**. It is usually composed by 64, 96, 128 or even more transducers

2. **Acquisition subsystem**. The hardware subsystem used for transducer excitation and data acquisition (represented by the box in the center). Nowadays, several electronic manufacturers have in their catalogues electronic boards and systems, which are small and can be easily used for our purposes. For example, National Instruments has 32-channel digitizer module capable of sampling on all channels at 50 MS/s with 12-bit resolution. The module is optimized for ultrasound applications [18]. Additionally, both multiplexer and bipolar programmable pulser are required. Specific architectures

depending on the type of acquisition strategy will be studied in the next section. 3. **Image generation subsystem**. It is the software system which can take place in any computational device (PC, laptop, . . . ) shown on the right side of Figure 10. These processes include the digital signal pre-processing of the received signals and filtering; beamforming of the image, delaying and adding signals according to emission and reception lenses, post-processing the image and its representation to properly show data on the screen. To achieve these tasks, the use of GPU's great power for parallel computing

will allow us to quickly and efficiently accelerate the algorithms.

to have two signals per coarray element for A and B codes.

acquisition and processing velocities and the system's frame rate.

*2.2.3. Experimental results*

**3. Ultrasonic imaging system**

**3.1. General system's overview**

depending on the type of application.

by three parts:

expense of doubling the hardware involved in the reception process.

One of the major drawbacks of Golay codes is that two shots are needed for each emitting element in order to complete both A and B codes respectively. In our work, Golay codes of length equal to 8 bits have been used, being *A*[8] = [+1 + 1 + 1 + 1 + 1 − 1 − 1 + 1] and *B*[8] = [+1 − 1 + 1 − 1 + 1 + 1 − 1 − 1], producing a gain of 24dB according to equation 4.

**Figure 8.** Golay encoding integration example

#### *2.2.2. Coarray for Golay encoding*

Golay codes, described previously, and minimum redundancy techniques can be combined. In order to illustrate how this can be done, Figure 8 shows an example using a 4R-SAFT (four receivers) [15] plus Golay codes. Here, two signals per coarray element are acquired and because Golay encoding needs to fire twice, A or B codes are alternated between shots.

This process is mathematically identical for the formerly presented strategies 2R-SAFT and kA-SAFT but with some particularities:

Strategies for Hardware Reduction on the Design of Portable Ultrasound Imaging Systems 11

