Phase unwrapping for 2-D blind deconvolution of ultrasound images

Single-image Bayesian Restoration and Multi-image Super-resolution Restoration for B-mode Ultrasound Using an Accurate System Model Involving Correlated Nature of the Speckle Noise

B-mode ultrasound is an essential part of radiological examinations due to its low cost, safety, and portability, but has the drawbacks of the speckle noise and output of most systems is two-dimensional (2D) cross sections. Image restoration techniques, using mathematical models for image degradation and noise, can be used to boost resolution (deconvolution) as well as to reduce the speckle. In this study, new single-image Bayesian restoration (BR) and multi-image super-resolution restoration (BSRR) methods are proposed for in-plane B-mode ultrasound images. The spatially correlated nature of the speckle was modeled, allowing for examination of two different models for BR and BSRR for uncorrelated Gaussian (BR-UG, BSRR-UG) and correlated Gaussian (BR-CG, BSRR-CG). The performances of these models were compared with common image restoration methods (Wiener filter, bilateral filtering, and anisotropic diffusion). Well-recognized metrics (peak signal-to-noise ratio, contrast-to-noise ratio, and normalized information density) were used for algorithm free-parameter estimation and objective evaluations. The methods were tested using superficial tissue (2D scan data collected from volunteers, tissue-mimicking resolutions, and breast phantoms). Improvement in image quality was assessed by experts using visual grading analysis. In general, BSRR-CG performed better than all other methods. A potential downside of BSRR-CG is increased computation time, which can be addressed by the use of high-performance graphics processing units (GPUs).

Portable ultrasound imaging system with super-resolution capabilities

This paper discusses an ultrasound technique where the echo signals from the array of transducer elements are compressed to as few as two RF channels while still in analog domain, with a much simplified front-end electronics. The method can achieve resolutions well beyond the diffraction limit, which is set by the excitation signal wavelength and numerical aperture of the imaging system. The fundamental principle that underlies this model based imaging technique is the preservation of the spatial frequency information content of the recorded echo signals with the help of pseudo-random apodization function followed by summation. A Verasonics V1 ultrasonic scanner is used to conduct experiments using an anechoic cyst made from gel phantom, immersed in degassed water. The estimated images were compared to those obtained using traditional B-mode delay-and-sum imaging available with the Verasonics V1 ultrasound machine. The estimated images using the proposed imaging technique showed a contrast ratio of 0.96 and Full-Width-Half-Maximum (FWHM) of about half the wavelength at a depth of 9.1 cm and at 1.875 MHz center frequency while the traditional delay and sum images had a contrast ratio of 0.62 and FWHM of about 5.5 wavelengths.

EEMD Domain AR Spectral Method for Mean Scatterer Spacing Estimation of Breast Tumors From Ultrasound Backscattered RF Data

We present a novel method for estimating the mean scatterer spacing (MSS) of breast tumors using ensemble empirical mode decomposition (EEMD) domain analysis of deconvolved backscattered radio frequency (RF) data. The autoregressive (AR) spectrum from which the MSS is estimated is obtained from the intrinsic mode functions (IMFs) due to regular scatterers embedded in RF data corrupted by the diffuse scatterers. The IMFs are chosen by giving priority to the presence of an enhanced fundamental harmonic and the presence of a greater number of higher harmonics in the AR spectrum estimated from the IMFs. The AR model order is chosen by minimizing the mean absolute percentage error (MAPE) criterion. In order to ensure that the backscattered data is indeed from a source of coherent scattering, we begin by performing a non-parametric Kolmogorov-Smirnov (K-S) classification test on the backscattered RF data. Deconvolution of the backscattered RF data, which have been classified by the K-S test as sources of significant coherent scattering, is done to reduce the system effect. EEMD domain analysis is then performed on the deconvolved data. The proposed method is able to recover the harmonics associated with the regular scatterers and overcomes many problems encountered while estimating the MSS from the AR spectrum of raw RF data. Using our technique, a mean absolute percentage error (MAPE) of 5.78% is obtained while estimating the MSS from simulated data, which is lower than that of the existing techniques. Our proposed method is shown to outperform the state of the art techniques, namely, singular spectrum analysis, generalized spectrum (GS), spectral autocorrelation (SAC), and modified SAC for different simulation conditions. The MSS for in vivo normal breast tissue is found to be 0.69 ± 0.04 mm; for benign and malignant tumors it is found to be 0.73 ± 0.03 and 0.79 ± 0.04 mm, respectively. The separation between the MSS values of normal and benign tissues for our proposed method is similar to the separations obtained for the conventional methods, but the separation between the MSS values for benign and malignant tissues for our proposed method is slightly higher than that for the conventional methods. When the MSS is used to classify breast tumors into benign and malignant, for a threshold-based classifier, the increase in specificity, accuracy, and area under curve are 18%, 19%, and 22%, respectively, and that for statistical classifiers are 9%, 13%, and 19%, respectively, from that of the next best existing technique.

Enhanced axial and lateral resolution using stabilized pulses

Ultrasound B-scan imaging systems operate under some well-known resolution limits. To improve resolution, the concept of stable pulses, having bounded inverse filters, was previously utilized for the lateral deconvolution. This framework has been extended to the axial direction, enabling a two-dimensional deconvolution. The modeling of the two-way response in the axial direction is discussed, and the deconvolution is performed in the in-phase quadrature data domain. Stable inverse filters are generated and applied for the deconvolution of the image data from Field II simulation, a tissue-mimicking phantom, and in vivo imaging of a carotid artery, where resolution enhancement is observed. Specifically, in simulation results, the resolution is enhanced by as many as 8.75 times laterally and 20.5 times axially considering the [Formula: see text] width of the autocorrelation of the envelope images.

Enhanced axial and lateral resolution using stabilized pulses

Ultrasound B-scan imaging systems operate under some well-known resolution limits. To improve resolution, the concept of stable pulses, having bounded inverse filters, was previously utilized for the lateral deconvolution. This framework has been extended to the axial direction, enabling a two-dimensional deconvolution. The modeling of the two-way response in the axial direction is discussed, and the deconvolution is performed in the in-phase quadrature data domain. Stable inverse filters are generated and applied for the deconvolution of the image data from Field II simulation, a tissue-mimicking phantom, and in vivo imaging of a carotid artery, where resolution enhancement is observed. Specifically, in simulation results, the resolution is enhanced by as many as 8.75 times laterally and 20.5 times axially considering the [Formula: see text] width of the autocorrelation of the envelope images.

Blind Deconvolution of Ultrasound Images Using l1 -Norm-Constrained Block-Based Damped Variable Step-Size Multichannel LMS Algorithm

The problem of improving the ultrasound image resolution by undoing the effect of convolution on backscattered radio-frequency (RF) data caused by the point spread function (PSF) of ultrasonic imaging system is one of the key problems in the reconstruction of the medical ultrasound images. In this paper, the tissue reflectivity functions (TRFs) are directly estimated from the noisy and nonstationary RF data using the block-based multichannel least-mean square ( l1 -bMCLMS) algorithm without any prior knowledge of the PSF. To account for the nonstationarity and incomplete acquisition problem of the ultrasound RF data a modified block-based cross-relation equation has been developed. An l1 -norm regularized cost function based on the proposed modified cross-relation equation is then formulated for blind estimation of the TRFs using the new l1 -bMCLMS algorithm. A damped variable step-size is also developed to compensate for the noise effect and to improve the convergence speed of the algorithm. The PSF is then estimated from multiple lateral blocks of RF data using the regularized multiple-input/output inverse theorem, which is known to be suitable for both minimum and nonminimum phase signals. The salient feature of the proposed method is that no basis function is required for TRFs and/or PSF. The efficacy of the proposed method is examined using the simulation/experimental phantom data and in vivo RF data and evaluated in terms of the quality metrics: resolution gain (RG), normalized projection misalignment (NPM), and shifted normalized mean square error (snMSE). The results show that the RG and NPM improvements of TRFs estimation of 0.12 ∼ 5.2 and 3.34 ∼ 22.82 dB, respectively, and the snMSE improvement of the PSF estimation of the order 10(2 ∼ 4) can be achieved in our technique as compared with the other techniques in the literature.

Superresolution imaging of scatterers in ultrasound B-scan imaging

A number of imaging systems exhibit speckle, which is caused by the interaction of a coherent pulse reflecting off of random reflectors. The limitations of these systems are quite serious because the speckle phenomenon creates a pattern of nulls and peaks from subresolvable scatterers or targets that are difficult to interpret. Another limitation of these pulse-echo imaging systems is that their resolution is dependent on the full spatial extent of the propagating pulse, usually several wavelengths in the axial or propagating dimension and typically longer in the transverse direction. This limits the spatial resolution to many multiples of the wavelength. This paper focuses on the particular case of ultrasound B-scan imaging and develops an inverse filter solution that eliminates both the speckle phenomenon and the poor resolution dependency on the pulse length and width to produce super-resolution ultrasound (SURUS) images. The key to the inverse filter is the creation of pulse shapes that have stable inverses. This is derived by use of the standard Z-transform and related properties. Although the focus of this paper is on examples from ultrasound imaging systems, the results are applicable to other pulse-echo imaging systems that also can exhibit speckle statistics.

Estimation of average speed of sound using deconvolution of medical ultrasound data

In diagnostic ultrasound imaging the speed of sound is assumed to be 1540 m/s in soft tissues. When the actual speed is different, the mismatch can lead to distortions in the acquired images and so reduce their clinical value. Therefore, the estimation of the true speed has been pursued not only because it enables image correction but also as a way of tissue characterisation. In this article, we present a novel way to measure the average speed of sound concurrently with performing image enhancement by deconvolution. This simultaneous capability, based on a single acquisition of ultrasound data, has not been reported in previous publications. Our algorithm works by conducting non-blind deconvolution of the reflection data with point-spread functions based on different speeds of sound. Using a search strategy, we select the speed that produces the best-possible restoration. The deconvolution operates on the beamformed uncompressed radio-frequency data, without any need to modify the hardware of the ultrasound machine. A conventional handling of the transducer array is all that is required in the data acquisition part of our proposed method: the data can be collected freehand, unlike most other estimation methods. We have tested our algorithm with simulations, in vitro phantoms with known and unknown speeds and in vivo scans. The estimation error was found to be +0.19 +/- 8.90 m/s (mean +/- standard deviation) for in vitro in-house phantoms whose speeds were also measured independently. In addition to the speed estimation, our method has also proved to be capable of simultaneously producing a better restoration of ultrasound images than deconvolution by an assumed speed of 1540 m/s, when this assumption is incorrect.

Predictive deconvolution and hybrid feature selection for computer-aided detection of prostate cancer

Computer-aided detection (CAD) schemes are decision making support tools, useful to overcome limitations of problematic clinical procedures. Trans-rectal ultrasound image based CAD would be extremely important to support prostate cancer diagnosis. An effective approach to realize a CAD scheme for this purpose is described in this work, employing a multi-feature kernel classification model based on generalized discriminant analysis. The mutual information of feature value and tissue pathological state is used to select features essential for tissue characterization. System-dependent effects are reduced through predictive deconvolution of the acquired radio-frequency signals. A clinical study, performed on ground truth images from biopsy findings, provides a comparison of the classification model applied before and after deconvolution, showing in the latter case a significant gain in accuracy and area under the receiver operating characteristic curve.

Two-dimensional blind Bayesian deconvolution of medical ultrasound images

A new approach to 2-D blind deconvolution of ultrasonic images in a Bayesian framework is presented. The radio-frequency image data are modeled as a convolution of the point-spread function and the tissue function, with additive white noise. The deconvolution algorithm is derived from statistical assumptions about the tissue function, the point-spread function, and the noise. It is solved as an iterative optimization problem. In each iteration, additional constraints are applied as a projection operator to further stabilize the process. The proposed method is an extension of the homomorphic deconvolution, which is used here only to compute the initial estimate of the point-spread function. Homomorphic deconvolution is based on the assumption that the point-spread function and the tissue function lie in different bands of the cepstrum domain, which is not completely true. This limiting constraint is relaxed in the subsequent iterative deconvolution. The deconvolution is applied globally to the complete radiofrequency image data. Thus, only the global part of the point-spread function is considered. This approach, together with the need for only a few iterations, makes the deconvolution potentially useful for real-time applications. Tests on phantom and clinical images have shown that the deconvolution gives stable results of clearly higher spatial resolution and better defined tissue structures than in the input images and than the results of the homomorphic deconvolution alone.

On approximation of smooth functions from samples of partial derivatives with application to phase unwrapping

This paper addresses the problem of approximating smooth bivariate functions from the samples of their partial derivatives. The approximation is carried out under the assumption that the subspace to which the functions to be recovered are supposed to belong, possesses an approximant in the form of a principal shift-invariant (PSI) subspace. Subsequently, the desired approximation is found as the element of the PSI subspace that fits the data the best in the (2)-sense. In order to alleviate the ill-posedness of the process of finding such a solution, we take advantage of the discrete nature of the problem under consideration. The proposed approach allows the explicit construction of a projection operator which maps the measured derivatives into a stable and unique approximation of the corresponding function. Moreover, the paper develops the concept of discrete PSI subspaces, which may be of relevance for several practical settings where one is given samples of a function instead of its continuously defined values. As a final point, the application of the proposed method to the problem of phase unwrapping in homomorphic deconvolution is described.

Blind deconvolution of medical ultrasound images: a parametric inverse filtering approach

The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a "hybridization" of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the "hybrid" approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolutioh algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used.

A New Method for Deblurring and Denoising of Medical Images using Complex Wavelet Transform

Deblurring in the presence of non-Gaussian noise is a hard problem, specially in ultrasonic and CT images. In this paper, a new method of image restoration, using complex wavelet transform, has been devised and applied to deblur in the presence of high speckle noise. It has been shown that the new method outperforms the Weiner filtering and Fourier-wavelet regularized deconvolution (ForWaRD) methods for both ultrasonic and CT images. Unlike Fourier and real wavelet transforms, complex wavelet transform is nearly shift-invariant. This gives complex wavelet transform an edge over other traditional methods when applied simultaneously for deblurring as well as denoising. The proposed method is independent of any assumption about the degradation process. It is adaptive, as it uses shrinkage function based on median and mean of absolute wavelet coefficient as well as standard deviation of wavelet coefficients. Its application on real spiral CT images of inner ear has shown a clear improvement over other methods.