Processing radio frequency ultrasound images: a robust method for local spectral features estimation by a spatially constrained parametric approach

Spectral estimation is a major component in studies aiming at characterizing biological tissues through the analysis of backscattered radio frequency (RF) ultrasonic signals and images. However, conventional spectral estimation techniques yield a well-known trade-off between spatial resolution and variance. The backscattered signals are stochastic by nature, so short-term local analysis results in a high variance of the estimates, which cannot efficiently be reduced through conventional spatial averaging. We address this issue by describing a spectral estimation technique that reduces the variance of the estimates (by smoothing the local estimates in spectrally homogeneous regions) while preserving spectral discontinuities (i.e., the smoothing is not performed across regions with different spectral contents). The proposed approach is set in a Bayesian framework and is based on local autoregressive (AR) estimation, constrained by smoothness priors. These smoothness priors are introduced through a Markov random field in which the associated potential functions are nonquadratic, allowing thereby to preserve discontinuity. The method is validated on simulated RF images and tested on echocardiographic images acquired in vivo. The results are compared to the estimates provided by the conventional Burg technique. These results clearly demonstrate the ability of the proposed approach to improve spectral estimation in terms of variance reduction and discontinuity detection.     

PSF dedicated to estimation of displacement vectors for tissue elasticity imaging with ultrasound

This paper investigates a new approach devoted to displacement vector estimation in ultrasound imaging. The main idea is to adapt the image formation to a given displacement estimation method to increase the precision of the estimation. The displacement is identified as the zero crossing of the phase of the complex cross-correlation between signals extracted from the lateral direction of the ultrasound RF image. For precise displacement estimation, a linearity of the phase slope is needed as well as a high phase slope. Consequently, a particular point spread function (PSF) dedicated to this estimator is designed. This PSF, showing oscillations in the lateral direction, leads to synthesis of lateral RF signals. The estimation is included in a 2-D displacement vector estimation method. The improvement of this approach is evaluated quantitatively by simulation studies. A comparison with a speckle tracking technique is also presented. The lateral oscillations improve both the speckle tracking estimation and our 2-D estimation method. Using our dedicated images, the precision of the estimation is improved by reducing the standard deviation of the lateral displacement error by a factor of 2 for speckle tracking and more than 3 with our method compared to using conventional images. Our method performs 7 times better than speckle tracking. Experimentally, the improvement in the case of a pure lateral translation reaches a factor of 7. Finally, the experimental feasibility of the 2-D displacement vector estimation is demonstrated on data acquired from a Cryogel phantom.     

Automatic spectral density estimation for random fields on a lattice via bootstrap

We consider the nonparametric estimation of spectral densities for second-order stationary random fields on a d-dimensional lattice. We discuss some drawbacks of standard methods and propose modified estimator classes with improved bias convergence rate, emphasizing the use of kernel methods and the choice of an optimal smoothing number. We prove the uniform consistency and study the uniform asymptotic distribution when the optimal smoothing number is estimated from the sampled data.     

2-D companding for noise reduction in strain imaging

Companding is a signal preprocessing technique for improving the precision of correlation-based time delay measurements. In strain imaging, companding is applied to warp 2-D or 3-D ultrasonic echo fields to improve coherence between data acquired before and after compression. It minimizes decorrelation errors, which are the dominant source of strain image noise. The word refers to a spatially variable signal scaling that compresses and expands waveforms acquired in an ultrasonic scan plane or volume. Temporal stretching by the applied strain is a single-scale (global), 1-D companding process that has been used successfully to reduce strain noise. This paper describes a two-scale (global and local), 2-D companding technique that is based on a sum-absolute-difference (SAD) algorithm for blood velocity estimation. Several experiments are presented that demonstrate improvements in target visibility for strain imaging. The results show that, if tissue motion can be confined to the scan plane of a linear array transducer, displacement variance can be reduced two orders of magnitude using 2-D local companding relative to temporal stretching.     

Three-dimensional blind deconvolution of ultrasound images

Three-dimensional ultrasound images are blurred by the ultrasound pulse through the convolution between the 3-D tissue signal and the 3-D pulse. The blurring reduces the spatial resolution of the 3-D ultrasound images and, consequently, their diagnostic value. This paper presents a method for 3-D blind homomorphic deconvolution of medical 3-D ultrasound images to improve their spatial resolution. The blind estimate of the 3-D pulse is necessary because the pulse changes in spatial extent and frequency composition as it passes through the tissues and because the pulse is not separable in its spatial dimensions. The method was tested on a 3-D image of a phantom with anechoic spheres of known size in a uniform diffuse scattering matrix. The spheres were clearly better defined and had volumes much closer to the true volume in the deconvolved image than in the original image     

Resolution in structured illumination microscopy: a probabilistic approach

Structured illumination can be employed to extend the lateral resolution of wide-field fluorescence microscopy. Since a structured illumination microscopy image is reconstructed from a series of several acquired images, we develop a modified formulation of the imaging response of the microscope and a probabilistic analysis to assess the resolution performance. We use this model to compare the fluorescence imaging performance of structured illumination techniques to confocal microscopy. Specifically, we examine the trade-off between achievable lateral resolution and signal-to-noise ratio when photon shot noise is dominant. We conclude that for a given photon budget, structured illumination invariably achieves better lateral resolution than confocal microscopy.     

Flexible depth-of-field imaging system using a spatial light modulator

A major problem of optical microscopes is their small depth-of-field (DOF), which hinders automation of micro object manipulation using visual feedback. Wavefront coding, a well-known method for extending DOF, is not suitable for direct application to micro object manipulation systems based on visual feedback owing to its expensive computational cost and due to a trade-off between the DOF and the image resolution properties. To solve such inherent problems, a flexible DOF imaging system using a spatial light modulator in the pupil plane is proposed. Especially, the trade-off relationship is quantitatively analyzed by experiments. Experimental results show that, for low criterion resolution, the DOF increases as the strength of the mask increases, while such a trend was not found for high criterion resolution. With high criterion resolution, the DOF decreases as the mask strength increases when high-resolution images are required. The results obtained can be used effectively to find the optimum mask strength given the desired image resolution.     

Scaling law for computational imaging using spherical optics

The resolution of a camera system determines the fidelity of visual features in captured images. Higher resolution implies greater fidelity and, thus, greater accuracy when performing automated vision tasks, such as object detection, recognition, and tracking. However, the resolution of any camera is fundamentally limited by geometric aberrations. In the past, it has generally been accepted that the resolution of lenses with geometric aberrations cannot be increased beyond a certain threshold. We derive an analytic scaling law showing that, for lenses with spherical aberrations, resolution can be increased beyond the aberration limit by applying a postcapture deblurring step. We then show that resolution can be further increased when image priors are introduced. Based on our analysis, we advocate for computational camera designs consisting of a spherical lens shared by several small planar sensors. We show example images captured with a proof-of-concept gigapixel camera, demonstrating that high resolution can be achieved with a compact form factor and low complexity. We conclude with an analysis on the trade-off between performance and complexity for computational imaging systems with spherical lenses.     

Methods of Multivariate Analysis

Nonparametric estimation of abrupt changes in a regression function involves choosing smoothing (bandwidth) parameters. The performance of estimation procedures depends heavily on this choice. So far, little attention has been paid to the crucial issue of choosing appropriate bandwidth parameters in practice. In this article we propose a bootstrap procedure for selecting the bandwidth parameters in a nonparametric two-step estimation method. This method results in a fully data-driven procedure for estimating a finite (but possibly unknown) number of changepoints in a regression function. We evaluate the performance of the data-driven procedure via a simulation study, which reveals that the fully automatic procedure performs quite well. As an illustration, we apply the procedure to some real data.     

基于变分贝叶斯多图像超分辨的平面复眼空间分辨率增强

平面复眼成像系统利用多个子孔径对场景进行成像,由于子孔径大小和图像传感器空间采样率的限制,各子孔径图像质量较差。如何融合多个子孔径图像来获得高分辨率图像是亟需解决的问题。多图像超分辨理论利用多幅具有互补信息的图像来重构高空间分辨率图像,然而现有理论通常采用过于简化的运动模型,这种简化的运动模型对平面复眼成像并不完全适用。若直接把现有多图像超分辨理论用于平面复眼分辨率增强,不准确的相对运动估计将降低图像分辨率增强性能。针对这些问题,本文在变分贝叶斯框架下改进了现有多图像超分辨理论中的运动模型,并把导出的联合估计算法用于平面复眼分辨率增强。仿真数据实验和真实复眼数据实验验证了推荐方法的正确性和有效性。     

Ultrasound speckle reduction using modified Gabor filters

B-mode ultrasound images are characterized by speckle artifact, which may make the interpretation of images difficult. One widely used method for ultrasound speckle reduction is the split spectrum processing (SSP), but the use of one-dimensional (1-D), narrow-band filters makes the resultant image experience a significant resolution loss. In order to overcome this critical drawback, we propose a novel method for speckle reduction in ultrasound medical imaging, which uses a bank of wideband 2-D directive filters, based on modified Gabor functions. Each filter is applied to the 2-D radio-frequency (RF) data, resulting in a B-mode image filtered in a given direction. The compounding of the filters outputs give rise to a final image in which speckle is reduced and the structure is enhanced. We have denoted this method as directive filtering (DF). Because the proposed filters have effectively the same bandwidth as the original image, it is possible to avoid the resolution loss caused by the use of narrow-band filters, as with SSP. The tests were carried out with both simulated and real clinical data. Using the signal-to-noise ratio (SNR) to quantify the amount of speckle of the ultrasound images, we have achieved an average SNR enhancement of 2.26 times with simulated data and 1.18 times with real clinical data.     

Three-dimensional ultrasound imaging system for prostate cancerdiagnosis and treatment

Prostate cancer is the most commonly diagnosed cancer in men in North America. Although two-dimensional (2-D) transrectal ultrasound imaging is widely used for the evaluation of prostate disease, it suffers from limitations that limit its use in diagnosis and therapy of prostate cancer. The use of conventional ultrasound requires that the diagnosticians mentally integrate a series of 2-D images in order to develop an impression of the three-dimensional (3-D) anatomy, and to estimate the volume of the prostate. This approach depends of the expertise of the physician resulting in variability. We have developed a 3-D ultrasound imaging approach that overcomes this problem. In this paper, we describe a 3-D ultrasound imaging system for use in prostate imaging and report on its performance. The system consists of a conventional ultrasound machine, a microcomputer with a video frame grabber, and a custom-built assembly for rotating the ultrasound transducer. A typical scan of 100 2-D B-mode images takes 8 s. These images are then reconstructed into a 3-D image, which can be displayed and interactively manipulated using 3-D visualization software. We also show that manual planimetry of prostates in the 3-D images can be used to estimate volumes in vitro with an accuracy of 2.6%, and a precision of 2.5%; and in vivo with 5.1% intra-observer variability and 11.4% interobserver variability. Thus, 3-D ultrasound imaging overcomes some of the limitations of conventional imaging of the prostate, and has great potential as a tool in the diagnosis and treatment of prostate disease     

Elasticity imaging using conventional and high-frame rate ultrasound imaging: experimental study

High-frame rate ultrasound imaging is necessary to track fast deformation in ultrasound elasticity imaging, but the image quality may be degraded. Previously, we investigated the performance of strain imaging using numerical models of conventional and ultrafast ultrasound imaging techniques. In this paper, we performed experimental studies to quantitatively evaluate the strain images and elasticity maps obtained using conventional and high frame rate ultrasound imaging methods. The experiments were carried out using point target and tissue mimicking phantoms. The experimental results were compared with the results of numerical simulation. Our experimental studies confirm that the signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and axial/lateral resolution of the displacement and strain images acquired using high-frame rate ultrasound imaging are slightly lower but comparable with those obtained using conventional imaging. Furthermore, the quality of elasticity images also exhibits similar trends. Thus, high-frame rate ultrasound imaging can be used reliably for static elasticity imaging to capture the internal tissue motion if the frame rate is critical.     

Lattice Distortion Analysis Directly from High Resolution Transmission Electron Microscopy Images—the LADIA Program Package

Direct strain mapping from high resolution transmission electron microscopy images is possible for coherent structures.At proper imaging conditions the intensity peaks in the image have a constant spatial relationship with the projected atom columns.This allows the determination of the geometry of the projected unit cell without comparison with image simulations.The fast procedure is particularly suited for the analysis of large areas.The software package LADIA is written in the PV-WAVE code and provides all necessary tools for image processing and analysis.Image iintensity peaks are determined by a cross-correlation technique,which avoids problems from noise in the low spatial frequency renage.The lower limit of strain that can be detected at a sampling rate of 44 pixels/nm is ≈2%.     

Comparison of 2-D speckle tracking and tissue Doppler imaging in an isolated rabbit heart model

Ultrasound strain imaging has been proposed to quantitatively assess myocardial contractility. Cross-correlation-based 2-D speckle tracking (ST) and auto-correlation-based tissue Doppler imaging (TDI) [often called Doppler tissue imaging (DTI)] are competitive ultrasound techniques for this application. Compared with 2-D ST, TDI, as a 1-D method, is sensitive to beam angle and suffers from low strain signal-to-noise ratio because a high pulse repetition frequency is required to avoid aliasing in velocity estimation. In addition, ST and TDI are fundamentally different in the way that physical parameters such as the mechanical strain are derived, resulting in different estimation accuracy and interpretation. In this study, we directly compared the accuracy of TDI and 2-D ST estimates of instantaneous axial normal strain and accumulated axial normal strain using a simulated heart. We then used an isolated rabbit heart model of acute ischemia produced by left descending anterior artery ligation to evaluate the performance of the two methods in detecting abnormal motion. Results showed that instantaneous axial normal strains derived using TDI (0.36% error) were less accurate with larger variance than those derived from 2-D ST (0.08% error) given the same spatial resolution. In addition to poorer accuracy, accumulated axial normal strain estimates derived using TDI suffered from bias, because the accumulation method for TDI cannot trace along the actual tissue displacement path. Finally, we demonstrated the advantage 2-D ST has over TDI to reduce dependency on beam angle for lesion detection by estimating strains based on the principal stretches and their corresponding principal axes.     

High-Resolution Digital Integral Photography by use of a Scanning Microlens Array

We suggest what we believe is a new three-dimensional (3-D) camera system for integral photography. Our method enables high-resolution 3-D imaging. In contrast to conventional integral photography, a moving microlens array (MLA) and a low-resolution camera are used. The intensity distribution in the MLA image plane is sampled sequentially by use of a pinhole array. The inversion problem from pseudoscopic to orthoscopic images is dealt with by electronic means. The new method is suitable for real-time 3-D imaging. We verified the new method experimentally. Integral photographs with a resolution of 3760 pixels x 2560 pixels (188 x 128 element images) are presented.     

Synthetic-aperture-radar imaging with a solid-state laser

We report the operation of an imaging Nd:YAG microchip-laser synthetic-aperture radar, with which we imaged two-dimensional (2-D) models of military targets. The images obtained showed spatial resolution significantly better than the diffraction limit of the real aperture in the along-track dimension. The signal processing is described, and the measurement sensitivity is both predicted and verified. In addition, 2-D images with high resolution in both dimensions were generated by using an asymmetric aperture to match the along-track synthetic-aperture resolution with the across-track diffraction-limited resolution.     

Phase-conjugate holographic system for high-resolution particle-image velocimetry

A novel holographic particle-image velocimeter system has been developed for the study of threedimensional (3-D) fluid velocity fields. The recording system produces 3-D particle images with a resolution, a signal-to-noise ratio, an accuracy, and derived velocity fields that are comparable to high-quality two-dimensional photographic particle-image velocimetry (PIV). The high image resolution is accomplished through the use of low f-number optics, a fringe-stabilized processing chemistry, and a phase conjugate play-back geometry that compensates for aberrations in the imaging system. In addition, the system employs a reference multiplexed, off-axis geometry for the determination of velocity directions with the cross-correlation technique, and a stereo camera geometry for the determination of the three velocity components. The combination of the imaging and reconstruction subsystems makes the analysis of volumetric PIV domains feasible.     

Angular strain estimation method for elastography

In the conventional cross-correlation-based strain estimation, there is a trade-off between the interpolation accuracy and the computational requirement. On the other hand, the autocorrelation-based method does not need interpolation, but it cannot estimate the wide range of displacements for elastography. We have developed a new strain estimator, called the angular strain estimation method, which does not need any interpolation and can estimate strain without restricting the range of displacements. The new method estimates strain utilizing complex correlation between correlated ultrasound signals from pre-and post-compression frames. From simulation and experiments, we found that the angular strain estimation method improves the accuracy and strain image quality compared to the conventional strain estimator using cross correlation with interpolation. Furthermore, it is computationally efficient and can be readily incorporated in ultrasound machines for rea -time elastography.