Blind deconvolution of ultrasound sequences using nonparametric local polynomial estimates of the pulse

Computation of Photoacoustic Absorber Size from Deconvolved Photoacoustic Signal Using Estimated System Impulse Response

Photoacoustic signal recorded by photoacoustic imaging system can be modeled as convolution of initial photoacoustic response by the photoacoustic absorber with the system impulse response. Our goal was to compute the size of photoacoustic absorber using the initial photoacoustic response, deconvolved from the recorded photoacoustic data. For deconvolution, we proposed to use the impulse response of the photoacoustic system, estimated using discrete wavelet transform based homomorphic filtering. The proposed method was implemented on experimentally acquired photoacoustic data generated by different phantoms and also verified by a simulation study involving photoacoustic targets, identical to the phantoms in experimental study. The photoacoustic system impulse response, which was estimated using the acquired photoacoustic signal corresponding to a lead pencil, was used to extract initial photoacoustic response corresponding to a mustard seed of 0.65 mm radius. The recovered radius values of the mustard seed, corresponding to the experimental and simulation studies were 0.6 mm and 0.7 mm.

Enhancement of Acoustic Microscopy Lateral Resolution: A Comparison Between Deep Learning and Two Deconvolution Methods

Scanning acoustic microscopy (SAM) provides high-resolution images of biological tissues. Since higher transducer frequencies limit penetration depth, image resolution enhancement techniques could help in maintaining sufficient lateral resolution without sacrificing penetration depth. Compared with existing SAM research, this work introduces two novelties. First, deep learning (DL) is used to improve lateral resolution of 180-MHz SAM images, comparing it with two deconvolution-based approaches. Second, 316-MHz images are used as ground truth in order to quantitatively evaluate image resolution enhancement. The samples used were mouse and rat brain sections. The results demonstrate that DL can closely approximate ground truth (NRMSE = 0.056 and PSNR = 28.4 dB) even with a relatively limited training set (four images, each smaller than 1 mm ×1 mm). This study suggests the high potential of using DL as a single image superresolution method in SAM.

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.

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.

Blind and semi-blind deblurring of natural images

A method for blind image deblurring is presented. The method only makes weak assumptions about the blurring filter and is able to undo a wide variety of blurring degradations. To overcome the ill-posedness of the blind image deblurring problem, the method includes a learning technique which initially focuses on the main edges of the image and gradually takes details into account. A new image prior, which includes a new edge detector, is used. The method is able to handle unconstrained blurs, but also allows the use of constraints or of prior information on the blurring filter, as well as the use of filters defined in a parametric manner. Furthermore, it works in both single-frame and multiframe scenarios. The use of constrained blur models appropriate to the problem at hand, and/or of multiframe scenarios, generally improves the deblurring results. Tests performed on monochrome and color images, with various synthetic and real-life degradations, without and with noise, in single-frame and multiframe scenarios, showed good results, both in subjective terms and in terms of the increase of signal to noise ratio (ISNR) measure. In comparisons with other state of the art methods, our method yields better results, and shows to be applicable to a much wider range of blurs.

A reduced complexity estimation algorithm for ultrasound images de-blurring

In this paper we propose a deconvolution technique for ultrasound images based on a Maximum Likelihood (ML) estimation procedure. In our approach the ultrasonic radio-frequency (RF) signal is considered as a sequence affected by Intersymbol Interference (ISI) and AWG noise. In order to reduce the computational cost, the estimation is performed with a reduced-state Viterbi algorithm. The channel effect is estimated in two different ways: either measuring the transducer response with an experimental setting or with blind homomorphic techniques. We observed an enhancement in image quality with respect to different metrics. Extensive tests were made to estimate the quantization alphabet that gives the best performances.

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.

Blind deconvolution of images using optimal sparse representations

The relative Newton algorithm, previously proposed for quasi-maximum likelihood blind source separation and blind deconvolution of one-dimensional signals is generalized for blind deconvolution of images. Smooth approximation of the absolute value is used as the nonlinear term for sparse sources. In addition, we propose a method of sparsification, which allows blind deconvolution of arbitrary sources, and show how to find optimal sparsifying transformations by supervised learning.

Phase unwrapping for 2-D blind deconvolution of ultrasound images

In most approaches to the problem of two-dimensional homomorphic deconvolution of ultrasound images, the estimation of a corresponding point-spread function (PSF) is necessarily the first stage in the process of image restoration. This estimation is usually performed in the Fourier domain by either successive or simultaneous estimation of the amplitude and phase of the Fourier transform (FT) of the PSE This paper addresses the problem of recovering the FT-phase of the PSF, which is an important reconstruction problem by itself. The purpose of this paper is twofold. First, it provides a theoretical framework, establishing that the FT-phase of the PSF can be effectively estimated by a proper smoothing of the FT-phase of the appropriate radio-frequency (RF) image. Second, it presents a novel approach to the estimation of the FT-phase of the PSF, by solving a continuous Poisson equation over a predefined smooth subspace, in contrast to the discrete Poisson equation solver used for the classical least mean squares phase unwrapping algorithms, followed by a smoothing procedure. The proposed approach is possible due to the distinct properties of the FT-phases, among which the most important property is the availability of precise values of their partial derivatives. This property overcomes the main disadvantage of the discrete schemes, which routinely use wrapped (principal) values of the phase in order to approximate its partial derivatives. Since such an approximation is feasible subject to the restriction that the partial phase differences do not exceed pi in absolute value, the discrete schemes perform satisfactory only for few practical situations. The proposed approach is shown to be independent of this restriction and, thus, it performs for a wider class of the phases with significantly lower errors. The main advantages of the novel method over the algorithms based on discrete schemes are demonstrated in a series of computer simulations and for in vivo measurements.

Robust deconvolution of high-frequency ultrasound images using higher-order spectral analysis and wavelets

Deconvolution of high-frequency (30-40 MHz) ultrasonic images of human skin was studied in vivo. Separate one-dimensional (1-D) functions for the axial and lateral profiles were first estimated using higher-order spectral methods. Subsequently, deconvolution was implemented us ing a regularized inverse Wiener filtering of the wavelet and scaling coefficients that were obtained after a wavelet decomposition of the RF signals. Deconvolution was first performed in the axial direction, then in the lateral direction. The methods were applied to data obtained from the skin of 16 volunteers using three different transducers. Significant improvements in both the axial and lateral resolutions were obtained in all the cases. Features such as hair follicles in the dermis and fingerprints on the surface of the finger were more clearly displayed in the processed images compared to the original images. The results indicate that the deconvolution method using higher-order spectral methods and wavelet analysis could significantly improve the quality of high-frequency ultrasonic skin images.

Robust estimation of ultrasound pulses using outlier-resistant de-noising

A different approach to the problem of estimation of the ultrasound pulse spectrum, which usually arises as a part of ultrasound image restoration algorithms, is presented. It is shown that this estimation problem can be reformulated in terms of a de-noising problem. In this formulation, the log-spectrum of a radio-frequency line (RF-line) is viewed as a noisy measurement of the signal that needs to be estimated, i.e., the ultrasound pulse log-spectrum. The log-spectrum of the tissue reflectivity function (i.e., tissue response) is considered as the noise to be rejected. The contribution of the paper is twofold. First, it provides statistical description of the reflectivity function log-spectrum for the case, when the samples of the reflectivity function are independent identically distributed (i.i.d.) Gaussian random variables. Moreover, it is shown that the problem of the pulse spectrum recovery is essentially a de-noising problem. Consequently, it is suggested to solve the problem within the framework of the de-noising by wavelet shrinkage. Second, a computationally efficient algorithm is proposed for the pulse-spectrum estimation, which can be viewed as a modified version of the classical Donoho's three-step de-noising procedure. This modification is necessary, because of specific properties of the noise to be rejected. It is shown, that whenever the samples of the reflectivity function can be assumed to be i.i.d. Gaussian random variables, the samples of its log-spectrum obey the Fisher-Tippet distribution. For this type of noise, straightforward implementation of the standard de-noising can cause serious estimation errors. In order to overcome this difficulty, an outlier-resistant de-noising is performed. The unique properties of this modified de-noising algorithm allow estimating the pulse spectrum adaptively to its properties, as they are continuously influenced by the frequency-dependent attenuation process. The performance of the proposed algorithm is examined in a series of computer-simulations. It is shown that this algorithm, developed on the assumption of the "Gaussian" reflectivity function, remains applicable for broader classes of distributions. The results obtained in a series of in vivo experiments reveal superior performance of the novel approach over some of alternative estimation techniques, e.g., cepstrum-based estimation.

A high-resolution technique for ultrasound harmonic imaging using sparse representations in Gabor frames

Over the last few decades there were dramatic improvements in ultrasound imaging quality with the utilization of harmonic frequencies induced by both tissue and echo-contrast agents. The advantages of harmonic imaging cause rapid penetration of this modality to diverse clinical uses, among which myocardial perfusion determination seems to be the most important application. In order to effectively employ the information, comprised in the higher harmonics of the received signals, this information should be properly extracted. A commonly used method of harmonics separation is linear filtering. One of its main shortcomings is the inverse relationship between the detectability of the contrast agent and the axial resolution. In this paper, a novel, nonlinear technique is proposed for separating the harmonic components, contained in the received radio-frequency images. It is demonstrated that the harmonic separation can be efficiently performed by means of convex optimization. It performs the separation without affecting the image resolution. The procedure is based on the concepts of sparse signal representation in overcomplete signal bases. A special type of the sparse signal representation, that is especially suitable for the problem at hand, is explicitly described. The ability of the novel technique to acquire "un-masked," second (or higher) harmonic images is demonstrated in series of computer and phantom experiments.

Shift-invariant, DWT-based "projection" method for estimation of ultrasound pulse power spectrum

An approach to computing estimates of the ultrasound pulse spectrum from echo-ultrasound RF sequences, measured from biological tissues, is proposed. It is computed by a "projection" algorithm based on the Discrete Wavelet Transform (DWT) using averaging over a range of linear shifts. It is shown that the robust, shift invariant estimate of the ultrasound pulse power spectrum can be obtained by the projection of RF line log spectrum on an appropriately chosen subspace of L2(R) (i.e., the space of square-integrable functions) that is spanned by a redundant collection of compactly supported, scaling functions. This redundant set is formed from the traditional (in Wavelet analysis) orthogonal set of scaling functions and also by all its linear (discrete) shifts. A proof is given that the estimate, so obtained, could be viewed as the average of the orthogonal projections of the RF line log spectrum, computed for all significant linear shifts of the RF line log spectrum in frequency domain. It implies that the estimate is shift-invariant. A computationally efficient scheme is presented for calculating the estimate. Proof is given that the averaged, shift-invariant estimate can be obtained simply by a convolution with a kernel, which can be viewed as the discretized auto-correlation function of the scaling function, appropriate to the particular subspace being considered. It implies that the computational burden is at most O(n log2 n), where n is the problem size, making the estimate quite suitable for real-time processing. Because of the property of the wavelet transform to suppress polynomials of orders lower than the number of the vanishing moments of the wavelet used, the presented approach can be considered as a local polynomial fitting. This locality plays a crucial role in the performance of the algorithm, improving the robustness of the estimation. Moreover, it is shown that the "averaging" nature of the proposed estimation allows using (relatively) poorly regular wavelets (i.e., short filters), without affecting the estimation quality. The latter is of importance whenever the number of calculations is crucial.