Non-iterative Reconstruction Research Articles

Imaging of small penetrable obstacles based on the topological derivative method

PurposeThe purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.Design/methodology/approachThe method consists in rewriting the inverse reconstruction problem as a topology optimization problem and then to use the concept of topological derivatives to seek a higher-order asymptotic expansion for the topologically perturbed cost functional. Such expansion is truncated and then minimized with respect to the parameters under consideration, which leads to noniterative second-order reconstruction algorithms.FindingsIn this paper, the authors develop two different classes of noniterative second-order reconstruction algorithms that are able to accurately recover the unknown penetrable obstacles from partial measurements of a field generated by incident waves.Originality/valueThe current paper is a pioneer work in developing a reconstruction method entirely based on topological derivatives for solving an inverse scattering problem with penetrable obstacles. Both algorithms proposed here are able to return the number, location and size of multiple hidden and unknown obstacles in just one step. In summary, the main features of these algorithms lie in the fact that they are noniterative and thus, very robust with respect to noisy data as well as independent of initial guesses.

Non-iterative complex wave-field reconstruction based on Kramers–Kronig relations

A non-iterative and non-interferometric computational imaging method to reconstruct a complex wave field called synthetic aperture imaging based on Kramers–Kronig relations (KKSAI) is reported. By collecting images through a modified microscope system with pupil modulation capability, we show that the phase and amplitude profile of the sample at pupil limited resolution can be extracted from as few as two intensity images by using Kramers–Kronig (KK) relations. It is established that as long as each subaperture’s edge crosses the pupil center, the collected raw images are mathematically analogous to off-axis holograms. This in turn allows us to adapt a recently reported KK-relations-based phase recovery framework in off-axis holography for use in KKSAI. KKSAI is non-iterative, free of parameter tuning, and applicable to a wider range of samples. Simulation and experiment results have proved that it has much lower computational burden and achieves the best reconstruction quality when compared with two existing phase imaging methods.

A stable non-iterative reconstruction algorithm for the acoustic inverse boundary value problem

<p style='text-indent:20px;'>We present a non-iterative algorithm to reconstruct the isotropic acoustic wave speed from the measurement of the Neumann-to-Dirichlet map. The algorithm is designed based on the boundary control method and involves only computations that are stable. We prove the convergence of the algorithm and present its numerical implementation. The effectiveness of the algorithm is validated on both constant speed and variable speed, with full and partial boundary measurement as well as different levels of noise.</p>

Convolutional neural network based non-iterative reconstruction for accelerating neutron tomography * * This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce

Neutron computed tomography (NCT), a 3D non-destructive characterization technique, is carried out at nuclear reactor or spallation neutron source-based user facilities. Because neutrons are not severely attenuated by heavy elements and are sensitive to light elements like hydrogen, neutron radiography and computed tomography offer a complementary contrast to x-ray CT conducted at a synchrotron user facility. However, compared to synchrotron x-ray CT, the acquisition time for an NCT scan can be orders of magnitude higher due to lower source flux, low detector efficiency and the need to collect a large number of projection images for a high-quality reconstruction when using conventional algorithms. As a result of the long scan times for NCT, the number and type of experiments that can be conducted at a user facility is severely restricted. Recently, several deep convolutional neural network (DCNN) based algorithms have been introduced in the context of accelerating CT scans that can enable high quality reconstructions from sparse-view data. In this paper, we introduce DCNN algorithms to obtain high-quality reconstructions from sparse-view and low signal-to-noise ratio NCT data-sets thereby enabling accelerated scans. Our method is based on the supervised learning strategy of training a DCNN to map a low-quality reconstruction from sparse-view data to a higher quality reconstruction. Specifically, we evaluate the performance of two popular DCNN architectures—one based on using patches for training and the other on using the full images for training. We observe that both the DCNN architectures offer improvements in performance over classical multi-layer perceptron as well as conventional CT reconstruction algorithms. Our results illustrate that the DCNN can be a powerful tool to obtain high-quality NCT reconstructions from sparse-view data thereby enabling accelerated NCT scans for increasing user-facility throughput or enabling high-resolution time-resolved NCT scans.

Topological sensitivity method for reconstruction of the spatial component in the source term of a time-fractional diffusion equation

In the paper, an inverse source problem for a time-fractional diffusion equation is formulated and proved. The topological sensitivity analysis method is presented. The considered problem is formulated as a topology optimization one. The proposed process leads to a non-iterative reconstruction algorithm can be applied for large class of cost functional. The unknown shape of the term source support is reconstructed using a level-set curve of the topological gradient. Several numerical simulations are presented to show the efficiency and the accuracy of the algorithm.

Superresolved image reconstruction in FZA lensless camera by color-channel synthesis.

The Fresnel-zone-aperture lensless camera using a fringe-scanning technique allows non-iterative well-conditioned image reconstruction; however, the spatial resolution is limited by the mathematical reconstruction model that ignores diffraction. To solve this resolution problem, we propose a novel image-reconstruction algorithm using the wave-optics-based design of the deconvolution filter and color-channel image synthesis. We verify a two-fold improvement of the effective angular resolution by conducting numerical simulations and optical experiments with a prototype.

Iterative versus non-iterative image reconstruction methods for sparse magnetic resonance imaging.

Magnetic resonance imaging (MRI) using under-sampled k-space data is a common method to shorten the imaging time. Iterative Bayesian algorithms are usually used for its image reconstruction. This paper compares an iterative Bayesian image reconstruction method that uses both spatial and temporal constraints and a non-iterative reconstruction algorithm that does not use temporal constraints. Three patient studies are performed. It is interesting to notice that the images reconstructed by the iterative Bayesian algorithm may introduce more bias than the non-iterative algorithm, even though the images provided by the iterative Bayesian algorithm look less noisy. The bias can be reduced by decreasing the influence of the temporal constraints.

Microlocally accurate solution of the inverse source problem of thermoacoustic tomography

We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Under the assumption of constant speed of sound we develop an explicit non-iterative reconstruction procedure that recovers the Radon transform of the sought source, up to an infinitely smooth additive error term. The source then can be found by inverting the Radon transform. Our analysis is microlocal in nature and does not provide a norm estimate on the error in the so obtained image. However, numerical simulations show that this error is quite small in practical terms. We also present an asymptotically fast implementation of this procedure for the case when the data are given on a circular arc in 2D.

Identifying an unknown source term in a heat equation with time-dependent coefficients

ABSTRACT An inverse source problem for an n-dimensional heat equation with a time-varying coefficient is investigated. The spatially dependent component of a source function is determined from a measurement at the final time. The inverse problem is regularized by a mollification method. Hölder-type stability estimates are proved. Error estimates of Hölder type are also proved for regularized solutions for both a priori and a posteriori mollification parameter choice rules. A non-iterative reconstruction algorithm is proposed. Numerical examples in one and two dimensions are shown to illustrate the performance of the proposed method.

Optical Signal Phase Reconstruction Based on Temporal Transport-of-Intensity Equation

A non-iterative reconstruction scheme of phase modulated optical signals using dispersive media in direct-detection receiver is described. The phase retrieval is achieved by solving the temporal transport-of-intensity equation (TIE). The TIE is solved by the use of Fast Fourier Transform algorithm. Required carrier power added to the signal is examined and it is shown that carrier power larger by 2 to 3 dB than that needed in the Kramers–Kronig receiver. The carrier can be located inside the signal spectrum, lifting the condition that the signal needs to be single-sideband with tightly confined spectrum. The noise immunity in solving the TIE, which will be an issue in practical usage of the scheme, is also discussed.

Pollution Sources Reconstruction Based on the Topological Derivative Method

The topological derivative method is used to solve a pollution sources reconstruction problem governed by a steady-state convection-diffusion equation. To be more precise, we are dealing with a shape optimization problem which consists of reconstruction of a set of pollution sources in a fluid medium by measuring the concentration of the pollutants within some subregion of the reference domain. The shape functional measuring the misfit between the known data and solution of the state equation is minimized with respect to a set of ball-shaped geometrical subdomains representing the pollution sources. The necessary conditions for optimality are derived with the help of the topological derivative method which consists in expanding the shape functional asymptotically and then truncate it up to the second order term. The resulting expression is trivially minimized with respect to the parameters under consideration which leads to a noniterative second-order reconstruction algorithm. Two different cases are considered. Firstly, when the velocity of the leakages is given and we reconstruct the support of the unknown sources, including their locations and sizes. In the second case, we consider the size of the pollution sources to be known and find out the mean velocity of the leakages and their locations. Numerical examples are presented showing the capability of the proposed algorithm in reconstructing multiple pollution sources in both cases.

Non-iterative image reconstruction from sparse magnetic resonance imaging radial data without priors

The state-of-the-art approaches for image reconstruction using under-sampled k-space data are compressed sensing based. They are iterative algorithms that optimize objective functions with spatial and/or temporal constraints. This paper proposes a non-iterative algorithm to estimate the un-measured data and then to reconstruct the image with the efficient filtered backprojection algorithm. The feasibility of the proposed method is demonstrated with a patient magnetic resonance imaging study. The proposed method is also compared with the state-of-the-art iterative compressed-sensing image reconstruction method using the total-variation optimization norm.

Numerical solutions of the forward and inverse problems arising in diffuse optical tomography

Optical tomography is a typical non-invasive medical imaging technique, aiming to reconstruct the optical properties of tissues from boundary measurements by passing near infrared light through the tissues. We are concerned with the forward and inverse problems for a time-dependent diffusion equation model arising in diffuse optical tomography. To solve the forward problem, we develop a boundary integral equation method, and then derive a discretization scheme for the resulting system of boundary integral equations. As for the inverse problem, rather than the precise values of the optical parameters, we recover geometric information on unknown inclusions as anomalies where the optical properties are significantly different from the background medium. A noniterative reconstruction method with its rigorous justification is established. Finally, we present some numerical results that illustrate the efficiency and effectiveness of the proposed methods for both the forward and inverse problems.

Analytical Low-Dose CBCT Reconstruction Using Non-local Total Variation Regularization for Image Guided Radiation Therapy.

Purpose: Conventional iterative low-dose CBCT reconstruction techniques are slow and tend to over-smooth edges through uniform weighting of the image penalty gradient. In this study, we present a non-iterative analytical low-dose CBCT reconstruction technique by restoring the noisy low-dose CBCT projection with the non-local total variation (NLTV) method.Methods: We modeled the low-dose CBCT reconstruction as recovering high quality, high-dose CBCT x-ray projections (100 kVp, 1.6 mAs) from low-dose, noisy CBCT x-ray projections (100 kVp, 0.1 mAs). The restoration of CBCT projections was performed using the NLTV regularization method. In NLTV, the x-ray image is optimized by minimizing an energy function that penalizes gray-level difference between pair of pixels between noisy x-ray projection and denoising x-ray projection. After the noisy projection is restored by NLTV regularization, the standard FDK method was applied to generate the final reconstruction output.Results: Significant noise reduction was achieved comparing to original, noisy inputs while maintaining the image quality comparable to the high-dose CBCT projections. The experimental validations show the proposed NLTV algorithm can robustly restore the noise level of x-ray projection images while significantly improving the overall image quality. The improvement in normalized mean square error (NMSE) and peak signal-to-noise ratio (PSNR) measured from the non-local total variation-gradient projection (NLTV-GPSR) algorithm is noticeable compared to that of uncorrected low-dose CBCT images. Moreover, the difference of CNRs from the gains from the proposed algorithm is noticeable and comparable to high-dose CBCT.Conclusion: The proposed method successfully restores noise degraded, low-dose CBCT projections to high-dose projection quality. Such an outcome is a considerable improvement to the reconstruction result compared to the FDK-based method. In addition, a significant reduction in reconstruction time makes the proposed algorithm more attractive. This demonstrates the potential use of the proposed algorithm for clinical practice in radiotherapy.

FlatNet: Towards Photorealistic Scene Reconstruction From Lensless Measurements.

Lensless imaging has emerged as a potential solution towards realizing ultra-miniature cameras by eschewing the bulky lens in a traditional camera. Without a focusing lens, the lensless cameras rely on computational algorithms to recover the scenes from multiplexed measurements. However, the current iterative-optimization-based reconstruction algorithms produce noisier and perceptually poorer images. In this work, we propose a non-iterative deep learning-based reconstruction approach that results in orders of magnitude improvement in image quality for lensless reconstructions. Our approach, called FlatNet, lays down a framework for reconstructing high-quality photorealistic images from mask-based lensless cameras, where the camera's forward model formulation is known. FlatNet consists of two stages: (1) an inversion stage that maps the measurement into a space of intermediate reconstruction by learning parameters within the forward model formulation, and (2) a perceptual enhancement stage that improves the perceptual quality of this intermediate reconstruction. These stages are trained together in an end-to-end manner. We show high-quality reconstructions by performing extensive experiments on real and challenging scenes using two different types of lensless prototypes: one which uses a separable forward model and another, which uses a more general non-separable cropped-convolution model. Our end-to-end approach is fast, produces photorealistic reconstructions, and is easy to adopt for other mask-based lensless cameras.

A non-iterative reconstruction method for bioluminescence tomography

In this paper, we study an inverse source problem of the bioluminescence tomography in three dimensional case. Our aim is to reconstruct a bioluminescent source distribution within a body from the knowledge of the boundary measurements. The inverse source problem is reformulated as a topology optimization one minimizing an energy like type functional. It measures the difference between the solutions of two auxiliary boundary value problems. An asymptotic expansion of the considered functional with respect to a set of ball-shaped anomalies is computed using the topological sensitivity analysis method. The obtained theoretical result leads to build a non-iterative reconstruction algorithm. Finally, some numerical examples in 3D are presented in order to show the effectiveness of the devised reconstruction algorithm.

Topological Sensitivity Analysis and Kohn-Vogelius Formulation for Detecting a Rigid Inclusion in an Elastic Body

Our main interest in this work is to detect a rigid inclusion immersed in an isotropic elastic body $\Omega$ from a single pair of Cauchy data on $\partial \Omega$ in two dimensions. We want to completely characterize the unknown rigid inclusion, namely, the shape and the location of inclusion. The idea is to rewrite the inverse problem as an optimization problem, where an energy like functional is minimized with respect to the presence of a small inclusion. A topological sensitivity analysis is derived for an energy like functional. We proposed a non-iterative reconstruction algorithm based on the topological gradient concept. The unknown rigid inclusion is defined by a level curve of a scalar function. The proposed numerical approach is very robust with respect to noisy data. Finally, in order to show the efficiency and accuracy of the proposed algorithm, we present some numerical results.

A concept for single-shot volumetric fluorescence imaging via orthogonally polarized excitation lattices

The deconvolution of widefield fluorescence images provides only guesses of spatial frequency information along the optical axis due to the so called missing cone in the optical transfer function. Retaining the single-shot imaging speed of deconvolution microscopy while gaining access to missing cone information is thus highly desirable for microscopy of volumetric samples. Here, we present a concept that superimposes two orthogonally polarized excitation lattices with a phase-shift of p between them. In conjunction with a non-iterative image reconstruction algorithm this permits the restoration of missing cone information. We show how fluorescence anisotropy could be used as a method to encode and decode the patterns simultaneously and develop a rigorous theoretical framework for the method. Through in-silico experiments and imaging of fixed biological cells on a structured illumination microscope that emulates the proposed setup we validate the feasibility of the method.

Gridrec-MS: an algorithm for multi-slice tomography.

Advances in imaging systems and modeling allow for depth information to be retrieved from projections via virtual sectioning of the imaged object. Here we introduce a regridding method that explicitly and directly incorporates this information into a general and non-iterative tomographic reconstruction algorithm. The method is applicable to any imaging scheme that provides depth-resolved projections. Additionally, we show, via numerical simulations, that with this method the required number of projections for adequate angular sampling can be reduced.

Noniterative Hyperspectral Image Reconstruction From Compressive Fused Measurements

Compressive spectral imaging (CSI) enables the acquisition of spectral and spatial information of a scene using fewer projected measurements than traditional scanning approaches. Recently, research efforts have focused on obtaining high-resolution spectral images via expensive detectors and sophisticated CSI devices. Alternatively, high-resolution spectral images can be obtained using side information or fusion of compressed measurements, without significantly increasing acquisition costs. Indeed, these approaches retrieve improved resolution images applying iterative and computationally expensive algorithms. This paper proposes the fusion of compressed measurements obtained from two state-of-the-art CSI systems, the single-pixel camera (SPC) and the three-dimensional coded aperture snapshot imaging system (3D-CASSI), such that high-resolution images can be obtained by exploiting detailed spectra provided by the SPC and high spatial resolution of the 3D-CASSI. Specifically, a noniterative reconstruction algorithm is proposed, based on the fact that the spatial-spectral data lie in a low-dimensional subspace. In contrast to related works, the proposed approach relies on implementable CSI systems. Simulations and experimental results show the effectiveness of the proposed method compared to similar approaches, both in reconstruction quality and complexity. Specifically, the proposed method is up to 5.6 times faster than its counterparts and provides comparable quality of attained reconstructions.