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

Feasibility of Quantitative Tissue Characterization Using Novel Parameters Extracted From Photoacoustic Power Spectrum Considering Multiple Absorbers

Frequency domain analysis of radio frequency signal is performed to differentiate between different tissue categories in terms of spectral parameters. However, due to complex relationship between the absorber size and spectral parameters, they cannot be used for quantitative tissue characterization. In an earlier study, we showed that using linear relationship between absorber size and two new spectral parameters namely number of lobes and average lobe width, absorber size can be successfully recovered from photoacoustic signal generated by single absorber. As actual biological tissue contains multiple absorbers, in this study we extended the application of these two new spectral parameters for computing absorber size from signals generated by multiple PA absorbers. We revisited our analytical model to establish two new linear relationships between the absorber radius and number of lobes as well as average lobe width considering multiple absorbers with bandlimited acquisition. A simulation study was performed to validate these linear relationships. A retrospective ex vivo study, in which the spectral parameters were computed using multiwavelength photoacoustic signals, was performed with freshly exercised thyroid specimens from 38 actual human patients undergoing thyroidectomy after having a diagnosis of suspected thyroid lesions. From statistical analysis it is shown that both the parameters were significantly different between malignant and non-malignant thyroid and malignant and normal thyroid tissue. Performance of the supervised classification with the computed spectral parameters showed that the extracted parameters could be successfully used to differentiate malignant thyroid tissue from normal thyroid tissue with reasonable degree of accuracy.

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.

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.

A blind deconvolution approach to ultrasound imaging

In this paper, a single-input multiple-output (SIMO) channel model is introduced for the deconvolution process of ultrasound imaging; the ultrasound pulse is the single system input and tissue reflectivity functions are the channel impulse responses. A sparse regularized blind deconvolution model is developed by projecting the tissue reflectivity functions onto the null space of a cross-relation matrix and projecting the ultrasound pulse onto a low-resolution space. In this way, the computational load is greatly reduced and the estimation accuracy can be improved because the proposed deconvolution model contains fewer variables. Subsequently, an alternating direction method of multipliers (ADMM) algorithm is introduced to efficiently solve the proposed blind deconvolution problem. Finally, the performance of the proposed blind deconvolution method is examined using both computer-simulated data and practical in vitro and in vivo data. The results show a great improvement in the quality of ultrasound images in terms of signal-to-noise ratio and spatial resolution gain.

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.

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 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.