Optimal apodization design for medical ultrasound using constrained least squares part II: simulation results

In the first part of this work, we introduced a novel general ultrasound apodization design method using constrained least squares (CLS). The technique allows for the design of system spatial impulse responses with narrow mainlobes and low sidelobes. In the linear constrained least squares (LCLS) formulation, the energy of the point spread function (PSF) outside a certain mainlobe boundary was minimized while maintaining a peak gain at the focus. In the quadratic constrained least squares (QCLS) formulation, the energy of the PSF outside a certain boundary was minimized, and the energy of the PSF inside the boundary was held constant. In this paper, we present simulation results that demonstrate the application of the CLS methods to obtain optimal system responses. We investigate the stability of the CLS apodization design methods with respect to errors in the assumed wave propagation speed. We also present simulation results that implement the CLS design techniques to improve cystic resolution. According to novel performance metrics, our apodization profiles improve cystic resolution by 3 dB to 10 dB over conventional apodizations such as the flat, Hamming, and Nuttall windows. We also show results using the CLS techniques to improve conventional depth of field (DOF).     

A novel beamformer design method for medical ultrasound. Part I: Theory

The design of transmit and receive aperture weightings is a critical step in the development of ultrasound imaging systems. Current design methods are generally iterative, and consequently time consuming and inexact. We describe a new and general ultrasound beamformer design method, the minimum sum squared error (MSSE) technique. The MSSE technique enables aperture design for arbitrary beam patterns (within fundamental limitations imposed by diffraction). It uses a linear algebra formulation to describe the system point spread function (psf) as a function of the aperture weightings. The sum squared error (SSE) between the system psf and the desired or goal psf is minimized, yielding the optimal aperture weightings. We present detailed analysis for continuous wave (CW) and broadband systems. We also discuss several possible applications of the technique, such as the design of aperture weightings that improve the system depth of field, generate limited diffraction transmit beams, and improve the correlation depth of field in translated aperture system geometries. Simulation results are presented in an accompanying paper.     

Cystic resolution: a performance metric for ultrasound imaging systems

This paper describes a metric that can be used to characterize the resolution of arbitrary broadband coherent imaging systems. The metric is particularly suited to medical ultrasound because it characterizes scanner performance using the contrast obtained by imaging anechoic cysts of various sizes that are embedded in a speckle-generating background, accounting for the effect of electronic noise. We present the theoretical derivation of the metric and provide simulation examples that demonstrate its utility. We use the metric to compare a low-cost, handheld, C-scan system under development in our laboratory to conventional ultrasound scanners. We also present the results of simulations that were designed to evaluate and optimize various parameters in our system, including the f/# and apodization windows. We investigate the impact of electronic noise on our system and quantify the tradeoffs associated with quantization in the analog to digital converter. Results indicate that an f/1 receive aperture combined with 10-bit precision and a signal-to-noise ratio (SNR) of 0 dB per channel would result in adequate image quality.     

Capon beamforming in medical ultrasound imaging with focused beams

Medical ultrasound imaging is conventionally done by insonifying the imaged medium with focused beams. The backscattered echoes are beamformed using delay-and-sum operations that cannot completely eliminate the contribution of signals backscattered by structures off the imaging beam to the beamsum. It leads to images with limited resolution and contrast. This paper presents an adaptation of the Capon beamformer algorithm to ultrasound medical imaging with focused beams. The strategy is to apply data-dependent weight functions to the imaging aperture. These weights act as lateral spatial filters that filter out off-axis signals. The weights are computed for each point in the imaged medium, from the statistical analysis of the signals backscattered by that point to the different elements of the imaging probe when insonifying it with different focused beams. Phantom and in vivo images are presented to illustrate the benefits of the Capon algorithm over the conventional delay and-sum approach. On heart sector images, the clutter in the heart chambers is decreased. The endocardium border is better defined. On abdominal linear array images, significant contrast and resolution enhancement are observed.     

Spatial encoding using a code division technique for fast ultrasound imaging

This paper describes a method for spatial encoding in synthetic transmit aperture ultrasound imaging. This allows several ultrasonic sources to be active simultaneously. The method is based on transmitting pseudorandom sequences to spatially encode the transmitters. The data can be decoded after only one transmission using the knowledge of the transmitted code sequences as opposed to other spatial encoding techniques, such as Hadamard or Golay encoding. This makes the method less sensitive to motion, and data can be acquired using fewer transmissions. The aim of this paper is to analyze the underlying theory and to test the feasibility in a physical system. The method has been evaluated in simulations using Field II in which the point-spread functions were simulated for different depths for a 7 MHz linear array transducer. A signal-to-noise ratio (SNR) simulation also was included in the study in which an improvement in SNR of approximately 1.5 dB was attained compared to the standard synthetic transmit aperture (STA) firing scheme. Considering the amount of energy transmitted, this value is low. A plausible explanation is given that is verified in simulation. The method also was tested in an experimental ultrasound scanner and compared to a synthetic transmit aperture ultrasound imaging scheme using a sinusoidal excitation. The performance of the proposed method was comparable to the reference with respect to axial and lateral resolution, but it displayed poorer contrast with sidelobe levels at approximately - 40 dB compared to the mainlobe.     

Efficient transmit beamforming in pulse-echo ultrasonic imaging

A high performance ultrasound imaging system requires accurate control of the amplitude of the array elements, as well as of the time delays between them, both in the transmit and receive modes. In transmission, conventional array aperture windowing implies a different driving voltage for each element of the array, an expensive solution for systems with a large number of channels. In this paper, we present a simple, versatile, and inexpensive beamforming method that operates the aperture windowing in the transmit mode, simply controlling the lengths of the electric pulses driving the array elements. Computer simulations and experimental measurements are presented for different types of arrays. They confirm that the proposed beamforming technique improves the contrast resolution of the imaging system, reducing the off-axis intensity of the radiated field pattern. Moreover, the axial resolution is slightly enhanced, because the overall length of the transmitted ultrasonic pulse is reduced.     

Frequency division transmission imaging and synthetic aperture reconstruction

In synthetic transmit aperture imaging only a few transducer elements are used in every transmission, which limits the signal-to-noise ratio (SNR). The penetration depth can be increased by using all transmitters in every transmission. In this paper, a method for exciting all transmitters in every transmission and separating them at the receiver is proposed. The coding is done by designing narrow-band linearly frequency modulated signals, which are approximately disjointed in the frequency domain and assigning one waveform to each transmitter. By designing a filterbank consisting of the matched filters corresponding to the excitation waveforms, the different transmitters can be decoded at the receiver. The matched filter of a specific waveform will allow information only from this waveform to pass through, thereby separating it from the other waveforms. This means that all transmitters can be used in every transmission, and the information from the different transmitters can be separated instantaneously. Compared to traditional synthetic transmit aperture (STA) imaging, in which the different transmitters are excited sequentially, more energy is transmitted in every transmission, and a better signal-to-noise-ratio is attained. The method has been tested in simulation, in which the resolution and contrast was compared to a standard synthetic transmit aperture system with a single sinusoid excitation. The resolution and contrast was comparable for the two systems. The method also has been tested using the experimental ultrasound scanner RASMUS. The resolution was evaluated using a string phantom. The method was compared to a conventional STA using both sinusoidal excitation and linear frequency modulated (FM) signals as excitation. The system using the FM signals and the frequency division approach yielded the same performance concerning both axial (of approximately equal to 3 wavelengths) and lateral resolution (of approximately equal to 4.5 wavelengths). A SNR measurement showed an increase in SNR of 6.5 dB compared to the system using the conventional STA method and FM signal excitation.     

Stress field forming of sector array transducers for vibro-acoustography

This paper presents a study of the stress field forming of sector array transducers for vibro-acoustography applications. The system point-spread function (PSF) is given in terms of the dynamic radiation stress exerted on a point target by a dual ultrasound beam with slightly different frequencies. The radiation stress is calculated by assuming that the resulting ultrasound beam is a plane wave. The stress is proportional to the product of the velocity potential of each incident ultrasound beam. The beamforming and stress field forming of sector array transducers are analyzed through linear acoustics. An expression for the velocity potential produced by sector array transducers is derived. The vibro-acoustography PSF is evaluated numerically. A comparison between the PSF of a sector array and a confocal transducers is presented. The compared characteristics of the PSF are sidelobe levels, transverse, and in-depth spatial resolution. Indeed, one motivation to study sector transducers is the fact the depth-of-field of these transducers should be smaller than that of same size confocal transducers. An experimental setup was used to validate the theoretical PSF of sector array transducers. Results show that the measured PSF is in good agreement with the theoretical predications. Vibro-acoustography images of a breast-phantom by both transducers are presented and discussed.     

Lateral RF image synthesis using a synthetic aperture imaging technique

The oscillating profile naturally present in ultrasound images has been shown to be extremely valuable in different applications, particularly in motion estimation. Recent studies have shown that it is possible to produce images with transverse oscillations (TOs) based on a specific type of beamforming. However, there is still a great difference between the nature of the lateral oscillations produced with current methods and the axial profile of ultrasound images. In this study, we propose to combine synthetic aperture imaging (synthetic transmit aperture, STA) using a specific beamformer in both transmit mode and receive mode combined with a heterodyning demodulation method to produce lateral radiofrequency signals (LRFs). The aim was to produce lateral signals as close as possible to conventional axial signals, which would make it possible to estimate lateral displacements with the same accuracy as in the axial direction. The feasibility of this approach was validated in simulation and experimentally on an ultrasound research platform, the Ultrasonix RP system. We show that the combination of STA and the heterodyning demodulation can divide the wavelength of the LRF signals by 4 and divide the width of the lateral envelope of the point spread function (PSF) by 2 compared with the previous approaches using beamforming in receive mode only. Finally, we also illustrate the potential of our beamforming for motion estimation compared with previous TO methods.     

Signal-to-noise comparison of deconvolution from wave-front sensing with traditional linear and speckle image reconstruction

It is well known that atmospheric turbulence severely degrades the performance of ground-based imaging systems. Techniques to overcome the effects of the atmosphere have been developing at a rapid pace over the past 10 years. These techniques can be grouped into two broad categories: predetection and postdetection techniques. A recent newcomer to the postdetection scene is deconvolution from wave-front sensing (DWFS). DWFS is a postdetection image-reconstruction technique that makes use of one feature of predetection techniques. A wave-front sensor (WFS) is used to record the wave-front phase distortion in the pupil of the telescope for each short-exposure image. The additional information provided by the WFS is used to estimate the system's point-spread function (PSF). The PSF is then used in conjunction with the ensemble of short-exposure images to obtain an estimate of the object intensity distribution through deconvolution. With the addition of DWFS to the suite of possible postdetection image-reconstruction techniques, it is natural to ask "How does DWFS compare with both traditional linear and speckle image-reconstruction techniques?" In the results we make a direct comparison based on a frequency-domain signal-to-noise-ratio performance metric. This metric is applied to each technique's image-reconstruction estimator. We find that DWFS nearly always results in improved performance over the estimators of traditional linear image reconstruction such as Wiener filtering. On the other hand, DWFS does not always outperform speckle-imaging techniques, and in cases that it does the improvement is small.     

Minimum variance beamforming applied to ultrasound imaging with a partially shaded aperture

Shadowing of an imaging aperture occurs when ultrasound beams are partially obstructed by an acoustically hard tissue, e.g., bone tissue. This effect leads to reduced resolution and, in some cases, geometrical distortion. In this paper, we initially introduce a binary apodization model to simulate effects of the shadowing on the point scatterers located close to a bone structure. Further, in a simulation study and an in vitro experiment, the minimum variance (MV) beamforming method is employed to image scatterers partly located in the shadow of bone. We show that the MV beamformer can result in a distorted image when the imaging aperture is highly obstructed by the bone structure. This distortion can be seen as an apparent lateral shift of the point spread function and a decrease in the sensitivity. Based on the signal power across the aperture, we adaptively determine the shadowed elements and discard their corresponding data from the covariance matrix to improve the MV beamformer performance. This modified MV beamformer can retain the resolution and compensate for the apparent lateral shifting and signal attenuation for the shadowed point scatterers.     

Use of modulated excitation signals in medical ultrasound. Part II: Design and performance for medical imaging applications

In the first paper, the superiority of linear FM signals was shown in terms of signal-to-noise ratio and robustness to tissue attenuation. This second paper in the series of three papers on the application of coded excitation signals in medical ultrasound presents design methods of linear FM signals and mismatched filters, in order to meet the higher demands on resolution in ultrasound imaging. It is shown that for the small time-bandwidth (TB) products available in ultrasound, the rectangular spectrum approximation is not valid, which reduces the effectiveness of weighting. Additionally, the distant range sidelobes are associated with the ripples of the spectrum amplitude and, thus, cannot be removed by weighting. Ripple reduction is achieved through amplitude or phase predistortion of the transmitted signals. Mismatched filters are designed to efficiently use the available bandwidth and at the same time to be insensitive to the transducer's impulse response. With these techniques, temporal sidelobes are kept below 60 to 100 dB, image contrast is improved by reducing the energy within the sidelobe region, and axial resolution is preserved. The method is evaluated first for resolution performance and axial sidelobes through simulations with the program Field II. A coded excitation ultrasound imaging system based on a commercial scanner and a 4 MHz probe driven by coded sequences is presented and used for the clinical evaluation of the coded excitation/compression scheme. The clinical images show a significant improvement in penetration depth and contrast, while they preserve both axial and lateral resolution. At the maximum acquisition depth of 15 cm, there is an improvement of more than 10 dB in the signal-to-noise ratio of the images. The paper also presents acquired images, using complementary Golay codes, that show the deleterious effects of attenuation on binary codes when processed with a matched filter, also confirmed by presented simulated images.     

Ultrasonic backscatter imaging by shear-wave-induced echo phase encoding of target locations

We present a novel method for ultrasound backscatter image formation wherein lateral resolution of the target is obtained by using traveling shear waves to encode the lateral position of targets in the phase of the received echo. We demonstrate that the phase modulation as a function of shear wavenumber can be expressed in terms of a Fourier transform of the lateral component of the target echogenicity. The inverse transform, obtained by measurements of the phase modulation over a range of shear wave spatial frequencies, yields the lateral scatterer distribution. Range data are recovered from time of flight as in conventional ultrasound, yielding a B-mode-like image. In contrast to conventional ultrasound imaging, where mechanical or electronic focusing is used and lateral resolution is determined by aperture size and wavelength, we demonstrate that lateral resolution using the proposed method is independent of the properties of the aperture. Lateral resolution of the target is achieved using a stationary, unfocused, single-element transducer. We present simulated images of targets of uniform and non-uniform shear modulus. Compounding for speckle reduction is demonstrated. Finally, we demonstrate image formation with an unfocused transducer in gelatin phantoms of uniform shear modulus.     

Contrast response analysis for medical ultrasound imaging

Traditional measures of spatial resolution are helpful but incomplete for characterizing the imaging performance of medical ultrasound systems because the challenge is not so much resolving strong point reflectors as limiting the impact of stronger scattering regions on weaker regions. This paper discusses the use of an alternative measure which is based on the ability of a system to accurately image an anechoic region surrounded by a uniform scattering medium. This measure, called contrast response, includes effects of both mainlobe width and sidelobe level. Since the impulse response of a linear system to a target is the convolution of the system spatial impulse response (beam pattern) and the target scattering function, the system output can be described by a three dimensional integral. The contrast response is defined as the ratio of this system output when the anechoic target is not present to the output when it is present, evaluated over a range of target sizes. Contrast response analysis is useful for both system design and performance comparison. Examples are presented which compare the performance of systems with different apodization functions and aperture sizes. This analysis approach suggests why the strong window functions popular in signal processing have not been used for apodization in medical ultrasound and why 256 channel systems have not demonstrated a dramatic performance improvement over 128 channel systems     

A new synthetic aperture focusing method to suppress the diffraction of ultrasound

Spatial resolution of an ultrasound image is limited by diffraction of ultrasound as it propagates along the axial direction. This paper proposes a method for reducing the diffraction spreading effect of ultrasound by using a synthetic aperture focusing (SAF) method that uses plane waves instead of spherical waves. The new method performs data acquisition and beamforming in the same manner as conventional SAF methods. The main difference is that all array elements are used on each firing to generate a plane wave, the traveling angle of which varies with the position of a receive subaperture. On reception, each scan line is formed by synthesizing RF samples acquired by relevant receive subapertures with delays to force the plane waves to meet at each imaging point. Theoretical analysis and computer simulation with infinite transmit aperture show that the proposed method is capable of suppressing the diffraction of ultrasound and especially causing the lateral beam width to remain unchanged beyond a certain depth determined by the size of a receive subaperture and the maximum traveling angle of plane waves. It is demonstrated that the proposed method is realizable using a linear array transducer. It is also shown that the lateral radiation pattern produced by the proposed method has smaller beam width than that using conventional SAF methods in the region of interest because it suppresses the diffraction of ultrasound.     

基于分段与识别技术的平面轮廓的精确重构

解决了由直线和圆弧构成的平面轮廓精确重构问题,满足轮廓各段之间位置连续以及相切条件.在正确识别角点、切点等特征点的基础上,提出了约束最小二乘算法,可精确求解带边界约束圆弧的重构问题.将圆弧边界约束条件分为5种类型:单点约束、双点约束、单切矢约束、单点单切矢约束和双切矢约束.针对每种类型给出了具体的计算公式.详细描述了轮廓精确重构的算法流程,可实现在全局误差控制下的精确重构,最后给出了运行实例,验证了算法的有效性.     

Volumetric real-time imaging using a CMUT ring array

A ring array provides a very suitable geometry for forward-looking volumetric intracardiac and intravascular ultrasound imaging. We fabricated an annular 64-element capacitive micromachined ultrasonic transducer (CMUT) array featuring a 10-MHz operating frequency and a 1.27-mm outer radius. A custom software suite was developed to run on a PC-based imaging system for real-time imaging using this device. This paper presents simulated and experimental imaging results for the described CMUT ring array. Three different imaging methods--flash, classic phased array (CPA), and synthetic phased array (SPA)--were used in the study. For SPA imaging, two techniques to improve the image quality--Hadamard coding and aperture weighting--were also applied. The results show that SPA with Hadamard coding and aperture weighting is a good option for ring-array imaging. Compared with CPA, it achieves better image resolution and comparable signal-to-noise ratio at a much faster image acquisition rate. Using this method, a fast frame rate of up to 463 volumes per second is achievable if limited only by the ultrasound time of flight; with the described system we reconstructed three cross-sectional images in real-time at 10 frames per second, which was limited by the computation time in synthetic beamforming.     

Synthetic-aperture imaging laser radar: laboratory demonstration and signal processing

The spatial resolution of a conventional imaging laser radar system is constrained by the diffraction limit of the telescope's aperture. We investigate a technique known as synthetic-aperture imaging laser radar (SAIL), which employs aperture synthesis with coherent laser radar to overcome the diffraction limit and achieve fine-resolution, long-range, two-dimensional imaging with modest aperture diameters. We detail our laboratory-scale SAIL testbed, digital signal-processing techniques, and image results. In particular, we report what we believe to be the first optical synthetic-aperture image of a fixed, diffusely scattering target with a moving aperture. A number of fine-resolution, well-focused SAIL images are shown, including both retroreflecting and diffuse scattering targets, with a comparison of resolution between real-aperture imaging and synthetic-aperture imaging. A general digital signal-processing solution to the laser waveform instability problem is described and demonstrated, involving both new algorithms and hardware elements. These algorithms are primarily data driven, without a priori knowledge of waveform and sensor position, representing a crucial step in developing a robust imaging system.     

Application of the Hotelling and ideal observers to detection and localization of exoplanets

The ideal linear discriminant or Hotelling observer is widely used for detection tasks and image-quality assessment in medical imaging, but it has had little application in other imaging fields. We apply it to detection of planets outside of our solar system with long-exposure images obtained from ground-based or space-based telescopes. The statistical limitations in this problem include Poisson noise arising mainly from the host star, electronic noise in the image detector, randomness or uncertainty in the point-spread function (PSF) of the telescope, and possibly a random background. PSF randomness is reduced but not eliminated by the use of adaptive optics. We concentrate here on the effects of Poisson and electronic noise, but we also show how to extend the calculation to include a random PSF. For the case where the PSF is known exactly, we compare the Hotelling observer to other observers commonly used for planet detection; comparison is based on receiver operating characteristic (ROC) and localization ROC (LROC) curves.     

Extended high-frame rate imaging method with limited-diffraction beams

Fast three-dimensional (3-D) ultrasound imaging is a technical challenge. Previously, a high-frame rate (HFR) imaging theory was developed in which a pulsed plane wave was used in transmission, and limited-diffraction array beam weightings were applied to received echo signals to produce a spatial Fourier transform of object function for 3-D image reconstruction. In this paper, the theory is extended to include explicitly various transmission schemes such as multiple limited-diffraction array beams and steered plane waves. A relationship between the limited-diffraction array beam weighting of received echo signals and a 2-D Fourier transform of the same signals over a transducer aperture is established. To verify the extended theory, computer simulations, in vitro experiments on phantoms, and in vivo experiments on the human kidney and heart were performed. Results show that image resolution and contrast are increased over a large field of view as more and more limited-diffraction array beams with different parameters or plane waves steered at different angles are used in transmissions. Thus, the method provides a continuous compromise between image quality and image frame rate that is inversely proportional to the number of transmissions used to obtain a single frame of image. From both simulations and experiments, the extended theory holds a great promise for future HFR 3-D imaging.