Non-iterative Image Reconstruction Research Articles

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.

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.

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.

Partial fourier shells trajectory for non-cartesian MRI

Non-Cartesian MRI acquisition has demonstrated various advantages in many clinical applications. The shells trajectory is a 3D non-Cartesian MRI acquisition technique that samples the k-space using a series of concentric shells to achieve efficient 3D isotropic acquisition. Partial Fourier acquisition is an acceleration technique that is widely used in Cartesian MRI. It exploits the conjugate symmetry of k-space measurement to reduce the number of k-space samples compared to full-k-space acquisition, without loss of spatial resolution. For a Cartesian MRI acquisition, the direction of partial Fourier acceleration is aligned either with the phase encoded or frequency encoded direction. In those cases, the underlying image matrix can be reconstructed from the undersampled k-space data using a non-iterative, homodyne reconstruction framework. However, designing a non-Cartesian acquisition trajectory that is compatible with non-iterative homodyne reconstruction is not nearly as straightforward as in the Cartesian case. One reason is the non-iterative homodyne reconstruction requires (slightly over) half of the k-space to be fully sampled. Since the direction of partial Fourier acceleration varies throughout the acquisition in the non-Cartesian trajectory, directly applying the same partial Fourier acquisition pattern (as in Cartesian acquisitions) to a non-Cartesian trajectory does not necessarily yield a continuous, physically-achievable trajectory. In this work, we develop an asymmetric shells trajectory with fully-automated trajectory and gradient waveform design to achieve partial Fourier acquisition for the shells trajectory. We then demonstrate a non-iterative image reconstruction framework for the proposed trajectory. Phantom and in vivo brain scans based on spoiled gradient echo (SPGR) shells and magnetization-prepared shells (MP-shells) were performed to test the proposed trajectory design and reconstruction method. Our phantom and in vivo results demonstrate that the proposed partial Fourier shells trajectory maintains the desirable image contrast and high sampling efficiency from the fully sampled shells, while further reducing data acquisition time.

Non-iterative model based image reconstruction of diffuse optical tomography based on DE and RTE in quality control of agricultural product studies

In a previous study, we developed the non-iterative image reconstruction based on diffusion equation. Within this research, we applied the same non-iterative algorithm scheme using radiative transfer equation. Basically, the non-iterative image reconstruction is a development of model based image reconstruction that implemented truncated singular value decomposition and L-curve analysis to solve the ill-posed problem. This algorithm reduces the computation time to reconstruct the cross-sectional area. As part of continuous development on agricultural application, optical tomography based quality control is offered. An experiment was conducted on potato to evaluate these two non-iterative algorithms. The object was illuminated by the near infrared source from 8 positions on the object boundary. In this experiment, we vary the position and the amount of epoxy on the object then we analyze the residual value between measurement and reconstructed boundary data. The reconstructions were performed in continuous-wave domain. Furthermore, we compared the residual value from diffuse optical tomography using diffusion equation and radiative transfer equation. The result of this study indicates that these algorithms are promising to detect the presence of epoxy on potato which is useful for quality control of agricultural products.

Images from Bits: Non-Iterative Image Reconstruction for Quanta Image Sensors.

A quanta image sensor (QIS) is a class of single-photon imaging devices that measure light intensity using oversampled binary observations. Because of the stochastic nature of the photon arrivals, data acquired by QIS is a massive stream of random binary bits. The goal of image reconstruction is to recover the underlying image from these bits. In this paper, we present a non-iterative image reconstruction algorithm for QIS. Unlike existing reconstruction methods that formulate the problem from an optimization perspective, the new algorithm directly recovers the images through a pair of nonlinear transformations and an off-the-shelf image denoising algorithm. By skipping the usual optimization procedure, we achieve orders of magnitude improvement in speed and even better image reconstruction quality. We validate the new algorithm on synthetic datasets, as well as real videos collected by one-bit single-photon avalanche diode (SPAD) cameras.

Partial fourier and parallel MR image reconstruction with integrated gradient nonlinearity correction.

To describe how integrated gradient nonlinearity (GNL) correction can be used within noniterative partial Fourier (homodyne) and parallel (SENSE and GRAPPA) MR image reconstruction strategies, and demonstrate that performing GNL correction during, rather than after, these routines mitigates the image blurring and resolution loss caused by postreconstruction image domain based GNL correction. Starting from partial Fourier and parallel magnetic resonance imaging signal models that explicitly account for GNL, noniterative image reconstruction strategies for each accelerated acquisition technique are derived under the same core mathematical assumptions as their standard counterparts. A series of phantom and in vivo experiments on retrospectively undersampled data were performed to investigate the spatial resolution benefit of integrated GNL correction over conventional postreconstruction correction. Phantom and in vivo results demonstrate that the integrated GNL correction reduces the image blurring introduced by the conventional GNL correction, while still correcting GNL-induced coarse-scale geometrical distortion. Images generated from undersampled data using the proposed integrated GNL strategies offer superior depiction of fine image detail, for example, phantom resolution inserts and anatomical tissue boundaries. Noniterative partial Fourier and parallel imaging reconstruction methods with integrated GNL correction reduce the resolution loss that occurs during conventional postreconstruction GNL correction while preserving the computational efficiency of standard reconstruction techniques. Magn Reson Med 75:2534-2544, 2016. © 2015 Wiley Periodicals, Inc.

Recovering Missing Slices of the Discrete Fourier Transform Using Ghosts

The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(n log(2) n) (for an n=N×N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT.

Noniterative image reconstruction method based on the subtraction of diffraction-intensity pattern

A noniterative image reconstruction method is proposed by the subtraction of diffraction intensity patterns based on the Fraunhofer diffraction theory. According to the linearity theorem of the Fourier transform, the process of the noniterative image reconstruction is performed by numerical calculation, that is, the object wavefront can be extracted by the subtraction of three diffraction intensity patterns of an object and two hybrid masks. Furthermore, the way the noise impacts the quality of the reconstructed image is evaluated and the noise is suppressed by a median filtering algorithm. The results certify that the reconstructed image is consistent with the image of the object. The method provides us with an easy way for retrieving the wavefront with high quality in a wide class of wave fields such as optical, X-ray, electron, and atomic waves.

Noniterative image reconstruction from photon-limited data with the use of self-cross-correlation

An algorithm for image reconstruction from a series of short-exposure images with the use of the self-cross-correlation (self-cross spectrum in the Fourier domain) between an observation g(x, y) and a truncated sub-image of it, p(x, y), is described. The truncated subimages are chosen to be the brightest region in the observed images and of size comparable with that of the average point-spread function. We find that this self-cross spectrum retains the first-order approximation diffraction-limited phase information of the unknown object and does not rely on the integration of the second-order phase difference or the third-order phase closure estimate. For the case in which the components of the object corresponding to the truncated subimage p(x, y) have edges, a method to extract these edges and then use them to recover the phase of the object is presented. Results from computer-simulated data and from real data show the effectiveness of the method.

Noise and spatial resolution of a real-time electrical impedance tomograph.

The Sheffield real-time electrical impedance tomograph produces 25 images per second, using 16 electrodes with adjacent-pair current drive and non-iterative image reconstruction. We describe the data acquisition timing of this instrument and present quantitative measurements of its signal-to-noise ratio and spatial resolution.