Fast Marching based Tissue Adaptive Delay Estimation for Aberration Corrected Delay and Sum Beamforming in Ultrasound Imaging.

Conventional ultrasound (US) imaging employs the delay and sum (DAS) receive beamforming with dynamic receive focus for image reconstruction due to its simplicity and robustness. However, the DAS beamforming follows a geometrical method of delay estimation with a spatially constant speed-of-sound (SoS) of 1540 m/s throughout the medium irrespective of the tissue in-homogeneity. This approximation leads to errors in delay estimations that accumulate with depth and degrades the resolution, contrast and overall accuracy of the US image. In this work, we propose a fast marching based DAS for focused transmissions which leverages the approximate SoS map to estimate the refraction corrected propagation delays for each pixel in the medium. The proposed approach is validated qualitatively and quantitatively for imaging depths of upto ∼ 11 cm through simulations, where fat layer-induced aberration is employed to alter the SoS in the medium. To the best of the authors' knowledge, this is the first work considering the effect of SoS on image quality for deeper imaging.Clinical relevance- The proposed approach when employed with an approximate SoS estimation technique can aid in overcoming the fat-induced signal aberrations and thereby in the accurate imaging of various pathologies of liver and abdomen.

Deep learning based correction of low performing pixel in computed tomography.

Low Performing Pixel (LPP)/bad pixel in CT detectors cause ring and streaks artifacts, structured non-uniformities and deterioration of the image quality. These artifacts make the image unusable for diagnostic purposes. A missing/defective detector pixel translates to a channel missing across all views in sinogram domain and its effect gets spill over entire image in reconstruction domain as artifacts. Most of the existing ring and streak removal algorithms perform correction only in the reconstructed image domain. In this work, we propose a supervised deep learning algorithm that operates in sinogram domain to remove distortions cause by the LPP. This method leverages CT scan geometry, including conjugate ray information to learn the interpolation in sinogram domain. While the experiments are designed to cover the entire detector space, we emphasize on LPPs near detector iso-center as these have most adverse impact on image quality specially if the LPPs fall on the high frequency region (bone-tissue interface). We demonstrated efficacy of the proposed method using data acquired on GE RevACT multi-slice CT system with flat-panel detector. Experimental results on head scans show significant reduction in ring artifacts regardless of LPP location in the detector geometry. We have simulated isolated LPPs accounting for 5% and 10% of total channels. Detailed statistical analysis illustrates approximately 5dB improvement in SNR in both sinogram and reconstruction domain as compared to classical bicubic and Lagrange interpolation methods. Also, with reduction in ring and streak artifacts, the perceptual image quality is improved across all the test images.

Constraints in dual phase shifting interferometry.

The paper presents approaches based on traditional phase shifting, flexible least-squares, and signal processing methods in dual phase shifting interferometry primarily applied to holographic moiré for retrieving multiple phases. The study reveals that these methods cannot be applied straightforward to retrieve phase information and discusses the constraints associated with these methods. Since the signal processing method is the most efficient among these approaches, the paper discusses significant issues involved in the successful implementation of the concept. In this approach the knowledge of the pair of phase steps is of paramount interest. Thus the paper discusses the choice of the pair of phase steps that can be applied to the phase shifting devices (PZTs) in the presence of noise. In this context, we present a theoretical study using Cramér-Rao bound with respect to the selection of the pair of phase step values in the presence of noise.

Estimation of multiple phases in interferometry in the presence of nonlinear arbitrary phase steps.

A phase shifting device (PZT) which is commonly applied in interferometry for phase measurement, unfortunately, has a nonlinear response to the applied voltage. In certain configurations such as, holographic moiré, where incorporation of two PZTs yields multiple phase information regarding the two orthogonal displacement components, the nonlinear response of the two PZTs yields highly erroneous result. In this context, we present for the first time a method for compensating multiple nonlinearities in the PZTs. Experimental results show the feasibility of the proposed method. The statistical performance of this method is also verified by comparing with the Cramér-Rao lower bound.

Super-resolution Fourier transform method in phase shifting interferometry.

The paper proposes a super-resolution Fourier transform method for phase estimation in phase shifting interferometry. Incorporation of a super-resolution technique before the application of Fourier transform significantly enhances the resolution capability of the proposed method. The other salient features of the method lie in its ability to handle multiple harmonics, PZT miscalibration, and arbitrary phase steps in the optical configuration. The method does not need addition of any carrier fringes to separate the spectral contents in the intensity fringes. The proposed concept thus overcomes the limitations of other methods based on Fourier transform techniques. The robustness of the proposed method is studied in the presence of noise.

An integral approach to phase shifting interferometry using a super-resolution frequency estimation method.

The objective of this paper is to describe an integral approach - based on the use of a super-resolution frequency estimation method - to phase shifting interferometry, starting from phase step estimation to phase evaluation at each point on the object surface. Denoising is also taken into consideration for the case of a signal contaminated with white Gaussian noise. The other significant features of the proposal are that it caters to the presence of multiple PZTs in an optical configuration, is capable of determining An integral approach to phase shifting the harmonic content in the signal and effectively eliminating their influence on measurement, is insensitive to errors arising from PZT miscalibration, is applicable to spherical beams, and is a robust performer even in the presence of white Gaussian intensity noise.

Statistical study of generalized nonlinear phase step estimation methods in phase-shifting interferometry.

Signal processing methods based on maximum-likelihood theory, discrete chirp Fourier transform, and spectral estimation methods have enabled accurate measurement of phase in phase-shifting interferometry in the presence of nonlinear response of the piezoelectric transducer to the applied voltage. We present the statistical study of these generalized nonlinear phase step estimation methods to identify the best method by deriving the Cramér-Rao bound. We also address important aspects of these methods for implementation in practical applications and compare the performance of the best-identified method with other bench marking algorithms in the presence of harmonics and noise.

Statistical study and experimental verification of high-resolution methods in phase-shifting interferometry.

The introduction of high-resolution phase-shifting interferometry methods such as annihilation filter, state space, multiple-signal classification, minimum norm, estimation of signal parameter via rotational invariance, and maximum-likelihood estimator have enabled the estimation of phase in an interferogram in the presence of harmonics and noise. These methods are also effective in holographic moiré where incorporating two piezoelectric transducers (PZTs) yields two orthogonal displacement components simultaneously. Typically, when these methods are used, the first step involves estimating the phase steps pixelwise; then the interference phase distribution is computed by designing a Vandermonde system of equations. In this context, we present a statistical study of these methods for the case of single and dual PZTs. The performance of these methods is also compared with other conventional benchmarking algorithms involving the single PZT. The paper also discusses the significant issue of an allowable pair of phase steps in the presence of noise using a robust statistical tool such as the Cramér-Rao bound. Furthermore, experimental validations of these high-resolution methods are presented for the estimation of single phase in holographic interferometry and for the estimation of multiple phases in holographic moiré.

Predicting phase steps in phase-shifting interferometry in the presence of noise and harmonics.

A novel method for estimating pixelwise phase step values in phase-shifting interferometry is presented. The method is based on the linear prediction property of the intensity fringes recorded temporally at a pixel on the charged-coupled device. The salient features of the method lie in their ability to handle linear miscalibration errors, to compensate for the presence of harmonics in an optical configuration and detector nonlinearity, and to allow for the use of arbitrary phase steps. The robustness of the proposed method is studied in the presence of noise and a comparison with several benchmarking algorithms is performed. The simulation results show the efficiency of the algorithm in retrieving the wrapped phase.

Phase-shifting interferometry in the presence of nonlinear phase steps, harmonics, and noise.

A phase-shifting piezo device commonly employed in phase-shifting interferometry exhibits a nonlinear response to applied voltage. Hence, a method for estimation of phase distribution in the presence of nonlinear phase steps is presented. The proposed method compensates for the harmonics present in the intensity fringe, allows the use of arbitrary phase-step values between 0 and tau rad, and does not impose constraints on the selection of particular phase-step values for minimizing nonlinearity and compensating for the harmonics. The comparison of the proposed method with other well-known benchmarking algorithms shows that our method is highly efficient and also works well in the presence of noise.

Chirp estimation in phase-shifting interferometry.

We propose a new approach for estimating the phase in the presence of a nonlinear response of a phase-shifting device: a piezoelectric transducer (PZT). The method is complemented well by the high resolution and the maximum likelihood estimation techniques in the estimation of the phase step and the nonlinear coefficient. The advantage of the proposed method is that it can be extended to the extraction of multiple phases in configurations involving multiple PZTs in the presence of nonlinearity. Symmetricity in the phase steps is not required in this method. Hence hysteresis of the PZT does not have any influence on the accuracy of the phase estimation. The effectiveness of the method is shown by experimental results.

Stochastic approach to data analysis in fluorescence correlation spectroscopy.

Fluorescence correlation spectroscopy (FCS) has emerged as a powerful technique for measuring low concentrations of fluorescent molecules and their diffusion constants. In FCS, the experimental data is conventionally fit using standard local search techniques, for example, the Marquardt-Levenberg (ML) algorithm. A prerequisite for these categories of algorithms is the sound knowledge of the behavior of fit parameters and in most cases good initial guesses for accurate fitting, otherwise leading to fitting artifacts. For known fit models and with user experience about the behavior of fit parameters, these local search algorithms work extremely well. However, for heterogeneous systems or where automated data analysis is a prerequisite, there is a need to apply a procedure, which treats FCS data fitting as a black box and generates reliable fit parameters with accuracy for the chosen model in hand. We present a computational approach to analyze FCS data by means of a stochastic algorithm for global search called PGSL, an acronym for Probabilistic Global Search Lausanne. This algorithm does not require any initial guesses and does the fitting in terms of searching for solutions by global sampling. It is flexible as well as computationally faster at the same time for multiparameter evaluations. We present the performance study of PGSL for two-component with triplet fits. The statistical study and the goodness of fit criterion for PGSL are also presented. The robustness of PGSL on noisy experimental data for parameter estimation is also verified. We further extend the scope of PGSL by a hybrid analysis wherein the output of PGSL is fed as initial guesses to ML. Reliability studies show that PGSL and the hybrid combination of both perform better than ML for various thresholds of the mean-squared error (MSE).

Resolution-enhanced Fourier transform method for the estimation of multiple phases in interferometry.

A phase shifting method based on high-resolution frequency estimation and Fourier transform technique is introduced. This method, also referred to as the eigenvector method, draws on the complementary strengths of both these methods. The salient feature of the method lies in its ability to handle nonsinusoidal wave-forms, multiple piezoelectric transducers, and arbitrary phase steps in an optical configuration. The method does not need the addition of carrier fringes to separate the spectral contents in the intensity fringes. The proposed concept thus overcomes the limitations of methods based on Fourier transform techniques. The robustness of the proposed method is studied in the presence of noise.

Model-based processing of a holographic moiré.

A state space model for the determination of dual phase distributions in a holographic moiré in the presence of nonsinusoidal waveforms, random noise, and miscalibration of the piezoelectric (PZT) devices is proposed. The extraction of these phase terms requires incorporating two PZTs into the moiré setup. A Toeplitz approximation method (TAM) is applied for phase determination, and modification to the Toeplitz covariance matrix formed from the phase-shifted moiré fringes by application of a denoising step in the state-feedback matrix is proposed. This step ensures that the phase terms can even be estimated at a signal-to-noise ratio much lower than that of the original TAM or by our previously suggested polynomial based method.

High-resolution frequency estimation technique for recovering phase distribution in interferometers.

An integral approach to phase measurement is presented. First, the use of a high-resolution technique for the pixelwise detection of phase steps is proposed. Next, the robustness of the algorithm that is developed is improved by incorporation of a denoising procedure during spectral estimation. The pixelwise knowledge of phase steps is then applied to the Vandermonde system of equations for retrieval of phase values at each pixel point. Conceptually, our proposal involves the design of an annihilating filter that has zeros at the frequencies associated with the polynomial that describes the fringe intensity. The parametric estimation of this annihilating filter yields the desired spectral information embedded in the signal, which in our case represents the phase steps. The proposed method offers the advantage of extracting the interference phase of nonsinusoidal waveforms in the presence of miscalibration error of the piezoelectric transducer. In addition, in contrast to previously reported methods, this method does not require the application of selective phase steps between data frames for nonsinusoidal waveforms.