**1. Introduction**

In the last decade, ultrasonic imaging systems have been an essential tool for diagnosis in medical and industrial applications, especially in the Non Destructive Testing area (NDT). Conventional ultrasonic imaging devices produce high quality images with good resolution and contrast. However, these machines are usually associated to a high cost in hardware resources, as well as in the time required for the data acquisition and processing stages. This fact hinders the development of good quality, compact and low-power systems that can operate in a wide range of real-time applications.

In this sense, the Synthetic Aperture techniques (SAFT) have demonstrated to be an effective method to achieve these goals, minimizing the size of the systems and accelerating the image acquisition processes. Consequently, both power consumption and overall cost of the systems can be reduced making possible their miniaturization and portability. Conventional SAFT techniques are based on the sequential activation in emission and reception of every transducer element. Once all acoustic signals have been stored in memory, a beamforming process is applied in a post-processing stage in order to focus the image dynamically in emission and reception, obtaining the maximum quality at each image pixel. Despite of this, conventional SAFT techniques present some inconveniences which are summarized in the following points:


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©2012 Romero-Laorden et al., licensee InTech. This is an open access chapter distributed under the terms of

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

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

and reception as Figure 12 suggests.

the radiation pattern could be written as:

*f*(*u*) =

*N*−1 ∑ *n*=0

*ftotal*(*z*) = *<sup>Z</sup>*{*cn*} =

in continuous wave is directly the DFT of the coarray [10].

populated what ensures a grating-lobe free radiation pattern.

the signals each time.

*anejkxnu* =

radiation pattern will be the product of two polynomials with degree *N* − 1:

2*N*−2 ∑ *n*=0

*cnz<sup>n</sup>* =

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 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

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

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

*N*−1 ∑ *n*=0

*anz<sup>n</sup>* .

*N*−1 ∑ *n*=0

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

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

Suppose a linear array with *N* elements. In far-field and assuming very narrow band signals,

*N*−1 ∑ *n*=0

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

*anejkndu* =

*N*−1 ∑ *n*=0

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

*an*(*ejkdu*)*<sup>n</sup>* (1)

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

245

*bnz<sup>n</sup>* (2)

are going to briefly review this mathematical concept and its principal implications.

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 real-time ultrasonic image.

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 the following aspects:


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 and future research developments.

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