Deconvolution methods for mitigation of transverse blurring in optical coherence tomography.

Imaging resolution in optical coherence tomography (OCT) is a key determinant for acquiring clinically useful optical biopsies of tissues. In contrast to light or confocal microscopy, the axial and transverse resolutions in OCT are independent and each can be analyzed individually. A method for mitigating transverse blurring and the apparent loss of transverse resolution in OCT by means of Gaussian beam deconvolution is presented. Such a method provides better representation of a specimen by using known physical parameters of a lens. To implement this method, deconvolution algorithms based on a focal-dependent kernel are investigated. First, the direct inverse problem is investigated using two types of regularization, truncated singular value decomposition, and Tikhonov. Second, an iterative expectation maximization algorithm, the Richardson-Lucy algorithm, with a beam-width-dependent iteration scheme is developed. A dynamically iterative Richardson-Lucy algorithm can reduce transverse blurring by providing an improvement in the transverse point-spread-function for sparse scattering samples in regions up to two times larger than the confocal region of the lens. These deblurring improvements inside and outside of the confocal region, which are validated experimentally, are possible without introducing new optical imaging hardware or acquiring multiple images of the same specimen. Implementation of this method in sparse scattering specimens, such as engineered tissues, has the potential to improve cellular detection and categorization.     

Point-source suppression for atmospheric wave extraction from airglow imaging measurements

Spectroscopic images of atmospheric chemiluminescent airglow contain fundamental diagnostic information about the structure and dynamics of the upper atmosphere. However, westward movement of stars causes non-negligible contamination in the two-dimensional horizontal wavenumber spectra extracted from all-sky airglow images. The conventional star-removing scheme is not effective in attenuating the star artifacts in the spectra of emission intensities of gravity wave perturbation, hindering the subsequent calculation of the angular spectra and the momentum fluxes of the profiles. To address this problem, a gradient-based edge detection algorithm for locating and attenuating the undesired star signal is developed. Comparatively, this algorithm is more effective than the conventional star-removing methods. The algorithm is validated in the context of experimentally obtained spectra.     

Optimal sensor array configuration in remote image formation.

Determination of optimal sensor configuration is an important issue in many remote imaging modalities, such as tomographic and interferometric imaging. In this paper, a statistical optimality criterion is defined and a search is performed over the space of candidate sensor locations to determine the configuration that optimizes the criterion over all candidates. To make the search process computationally feasible, a modified version of a previously proposed suboptimal backward greedy algorithm is used. A statistical framework is developed which allows for inclusion of several widely used image constraints. Computational complexity of the proposed algorithm is discussed and a fast implementation is described. Furthermore, upper bounds on the sum of the squared error of the proposed algorithm are derived. Connections of the method to the deterministic backward greedy algorithm for the subset selection problem are presented, and two application examples are described. Five compelling optimality criteria are considered, and their performance is investigated through numerical experiments for a tomographic imaging scenario. In all cases, it is verified that the configuration designed by the proposed algorithm performs better than wisely chosen alternatives.     

Asymptotically optimal blind estimation of multichannel images.

Optimal estimation of a two-dimensional (2-D) multichannel signal ideally decorrelates the data in both channel and space and weights the resulting coefficients according to their SNR. Many scenarios exist where the required second-order signal and noise statistics are not known in which the decorrelation is difficult or expensive to calculate. An asymptotically optimal estimation scheme proposed here uses a 2-D discrete wavelet transform to approximately decorrelate the signal in space and the discrete Fourier transform to decorrelate between channels. The coefficient weighting is replaced with a wavelet-domain thresholding operation to result in an efficient estimation scheme for both stationary and nonstationary signals. In contrast to optimal estimation, this new scheme does not require second-order signal statistics, making it well suited to many applications. In addition to providing vastly improved visual quality, the new estimator typically yields signal-to-noise ratio gains 12 dB or higher for hyperspectral imagery and functional magnetic resonance images.     

Multidimensional image reconstruction in astronomy

The goal of this article is to describe a unified approach based on the assumption of additive Gaussian noise and regularization theory that illustrates the flavor of such multidimensional image reconstruction problems and the associated challenges. Efficient iterative methods are described for the solution of these problems. Indeed, a crucial point in the solution to the problems considered in this article is the size of the data set and the need for efficient algorithms.     

A regularized inverse approach to ultrasonic pulse-echo imaging

An inverse-theoretic approach to ultrasonic pulse-echo imaging based on nonquadratic regularization is presented, and its effectiveness is investigated computationally by: 1) evaluating the quality of the reconstruction of speckle-based images as a function of the transmit-receive bandwidth and focal number of the transducer; 2) comparing the reconstructed images with those obtained by using conventional B-mode imaging. The L-curve and the generalized cross-validation methods were evaluated as automatic regularization parameter selection techniques. The inversion using regularization produced better results than conventional B-mode imaging for high signal-to-noise ratios (SNRs). A lower bound of 30 dB for the SNR was found for this study, below which several of the image features were lost during the reconstruction process in order to control the distortion due to the noise.     

Estimation of gravity wave momentum flux with spectroscopic imaging

Atmospheric gravity waves play a significant role in the dynamics and thermal balance of the upper atmosphere. In this paper, we present a novel technique for automated and robust calculation of momentum flux of high-frequency quasi-monochromatic wave components from spectroscopic imaging and horizontal radar wind measurements. Our approach uses the two-dimensional (2-D) cross periodogram of two consecutive Doppler-shifted time-differenced (TD) images to identify wave components and estimate intrinsic wave parameters. Besides estimating the average perturbation of dominant waves in the whole field of view, this technique applies 2-D short-space Fourier transform to the TD images to identify localized wave events. With the wave parameters acquired, the momentum flux carried by all vertically propagating wave components is calculated using an analytical model relating the measured intensity perturbation to the wave amplitude. This model is tested by comparing wave perturbation amplitudes inferred from spectroscopic images with those from sodium lidar temperature measurements. The proposed technique enables characterization of the variations in the direction and strength of gravity waves with high temporal resolution for each clear data-taking night. The nightly results provide statistical information for investigating seasonal and geographical variations in momentum flux of gravity waves.     

Tomographic Imaging of Dynamic Objects With the Ensemble Kalman Filter

We address the image formation of a dynamic object from projections by formulating it as a state estimation problem. The problem is solved with the ensemble Kalman filter (EnKF), a Monte Carlo algorithm that is computationally tractable when the state dimension is large. In this paper, we first rigorously address the convergence of the EnKF. Then, the effectiveness of the EnKF is demonstrated in a numerical experiment where a highly variable object is reconstructed from its projections, an imaging modality not yet explored with the EnKF. The results show that the EnKF can yield estimates of almost equal quality as the optimal Kalman filter but at a fraction of the computational effort. Further experiments explore the rate of convergence of the EnKF, its performance relative to an idealized particle filter, and implications of modeling the system dynamics as a random walk.