Fast Iterative Solving Method of Fuzzy Relational Equation and its Application to Image Compression/Reconstruction

The image reconstruction for Fourier-domain optical coherence tomography (FD-OCT) could be achieved by iterative methods, which offer a more accurate estimation than the traditional inverse discrete Fourier transform (IDFT) reconstruction. However, the existing iterative methods are mostly A-line-based and are developed on CPU, which causes slow reconstruction. Besides, A-line-based reconstruction makes the iterative methods incompatible with most existing image-level image processing techniques. In this paper, we proposed an iterative method that enables B-scan-based OCT image reconstruction, which has three major advantages: (1) Large-scale parallelism of the OCT dataset is achieved by using GPU acceleration. (2) A novel image-level cross-domain regularizer was developed, such that the image processing could be performed simultaneously during the image reconstruction; an enhanced image could be directly generated from the OCT interferogram. (3) The scalability of the proposed method was demonstrated for 3D OCT image reconstruction. Compared with the state-of-the-art (SOTA) iterative approaches, the proposed method achieves higher image quality with reduced computational time by orders of magnitude. To further show the image enhancement ability, a comparison was conducted between the proposed method and the conventional workflow, in which an IDFT reconstructed OCT image is later processed by a total variation-regularized denoising algorithm. The proposed method can achieve a better performance evaluated by metrics such as signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR), while the speed is improved by more than 30 times. Real-time image reconstruction at more than 20 B-scans per second was realized with a frame size of 4096 (axial) × 1000 (lateral), which showcases the great potential of the proposed method in real-world applications.

The quality of images produced by iterative image reconstruction methods is directly affected by the accuracy of the system model being used. Although the system response of an imaging system can be computed or measured with high accuracy, practical constraints on computation cost often force the adoption of various approximations to the system model to obtain a computationally efficient system matrix. These approximations inevitably cause artifacts in reconstructed image. In this work we propose a residual correction method for iterative reconstruction to reduce reconstruction artifact caused by the model inaccuracies. Unlike conventional iterative methods which assume that the system matrix is accurate, the proposed method reconstructs an initial image with an approximate system model and then corrects for the reconstruction artifacts by introducing a data correction term to compensate for the model inaccuracies. Computer simulation showed that the proposed method can significantly improve image quality in terms of objective function value compared to approximate algorithms, while it is computationally more efficient than the conventional method that uses the accurate system model at every iteration.

We have previously proposed an image reconstruction method to improve the image resolution in magnetic particle imaging. In that method, the image is reconstructed based on time-correlation information between the observed signal from magnetic nanoparticles and the corresponding system function. However, image blurring and image artifacts were not sufficiently improved under this method. Therefore, we proposed a new iterative image reconstruction method, in which the reconstructed image is iteratively estimated by correcting the difference between the analytically calculated signals from the reconstructed images and the observed signals during iteration. In this paper, to confirm the validity of this new proposed method, we performed experiments using the 3-D prototype system and numerical simulations based on the prototype system setup. The results achieved by the prototype system experiments showed that the image blurring was suppressed and the image quality improved as compared with the previous time-correlation reconstruction method.

Robust methods, such as Tikhonov regularization and Bounded data uncertainty, have been used extensively in relatively small problems involving dense matrices for many decades, but have not been used in large-scale iterative methods for image reconstruction in particle imaging until recently. In this case, robust methods may allow more accurate reconstruction of images in the presence of errors of both the energy measurement of the protons and ions but also in the estimated path taken by the proton or ion through the object. Robust systems may also be used when entire blocks of data are missing, or in low-dose reconstructions using a very small number of particles without substantial loss of image quality. In this contribution, we demonstrate that robust methods show great promise in proton/ion (particle) computed tomography (pCT), and, for the first time, that they can be proven to converge. Thus, the convergence of robust methods as well as benefits for reconstruction in uncertain systems is shown to constitute the main advantage for pCT reconstruction.

By accurately modeling the physics of photon transport into the projection and backprojection operations, iterative SPECT reconstruction methods can reduce the degrading effects of scatter, attenuation and the non-stationary spatial resolution of the camera. Unfortunately, iterative reconstruction methods have required very long computation times, predominately due to the complexity involved in modeling these degrading effects into the projection and backprojection operations. In this study, we describe an approach which allows SPECT iterative reconstruction algorithms to be implemented with a reduction in the number of computations needed. The idea is to pre-process the measured projection data to compensate for scatter and attenuation, as well as to transform the projection data to those which would have been obtained with a stationary system resolution. Results of simulation studies indicate that preprocessing the measured projection data reduces the number of computations needed to perform the projection and backprojection operations, and yields reconstructions which differ minimally from those obtained using the slower standard iterative approach of modeling both photon attenuation and nonstationary blurring in the projection and backprojection steps.

Optoacoustic tomography (OAT), also known as photoacoustic tomography, is a rapidly emerging hybrid imaging technique that possesses great potential for a wide range of biomedical imaging applications. In OAT, a laser is employed to illuminate the tissue of interest and acoustic signals are produced via the photoacoustic effect. From these data, an estimate of the distribution of the absorbed optical energy density within the tissue is reconstructed, referred to as the object function. This quantity is defined, in part, by the distribution of light fluence within the tissue that is established by the laser source. When performing three-dimensional imaging of large objects, such as a female human breast, it can be difficult to achieve a relatively uniform coverage of light fluence within the volume of interest when the position of the laser source is fixed. To circumvent this, researchers have proposed illumination schemes in which the relative position of the laser source and ultrasound probe is fixed, and both are rotated together to acquire a tomographic dataset. A problem with this rotating-illumination scheme is that the tomographic data are inconsistent; namely, the acoustic data recorded at each tomographic view angle (i.e., probe position) are produced by a distinct object function. In this work, the impact of this data inconsistency on image reconstruction accuracy is investigated systematically. This is accomplished by use of computer-simulation studies and application of mathematical results from the theory of microlocal analysis. These studies specify the set of image discontinuities that can be stably reconstructed with a nonstationary optical illumination setup. The study also includes a comparison of the ability of iterative and analytic image reconstruction methods to mitigate artifacts attributable to the data inconsistency.

A rapid and non-destructive method for quantifying biomolecules in Spirulina platensis via Fourier transform infrared – Attenuated total reflectance spectroscopy

Application of modified iterative method to simulate rainfall infiltration in unsaturated soils

Radial basis functions are popular basis for interpolating scattered data during the image reconstruction process in graphic analysis. In this context, the solution of a linear system of equations is required for each color (blue, red, green) and represents the most time-consuming operation. In this paper a two-level iterative algorithm is proposed to solve efficiently these linear systems of equations. This two-level algorithm consists of a preconditioned iterative method which enforces at each iteration a projection of the residual onto a suitable coarse space. This constraint is ensured by solving an auxiliary second-level problem at each iteration. Numerical results illustrate the convergence properties of the proposed method on a wide range of interpolation problems for image reconstruction.

In recent years, various approaches to overcome the problems associated with iterative statistical image reconstruction methods have been investigated, including issues such as slow convergence rate, costly computational time and nonuniform correction efficiency. A multiscale Bayesian image reconstruction algorithm based on a 1-D wavelet technique is proposed. In this approach, the authors first apply a wavelet transform to the sinogram measurements, which yields a multiresolution object representation. The image is reconstructed at the corresponding grid by the Bayesian image reconstruction algorithm for each scale level in the frequency space; the backprojector is also modified to match each corresponding resolution scale. After the low-frequency components of the image have been recovered sufficiently on the coarser scale level, the resulted image is used as the starting point for the finer level at a new iteration. An important feature in the authors' new approach is that the wavelet decomposition is carried out in the sinogram space, while multiple grids are also used in the reconstructed image space.

Adding prior knowledge to compressed sensing reconstruction can improve image reconstruction. In this work, two approaches are investigated to improve reconstruction of two-dimensional hyperpolarized (3)He lung ventilation images using prior knowledge. When compared against a standard compressed sensing reconstruction, the proposed methods allowed acquisition of images with higher under-sampling factors and reduction of the blurring effects that increase with higher reduction factors when fixed flip angles are used. These methods incorporate the prior knowledge of polarization decay of hyperpolarized (3)He and the mutual anatomical information from a registered (1)H image acquired in the same breath. Three times accelerated two-dimensional images reconstructed with compressed sensing and prior knowledge gave lower root-mean square error, than images reconstructed without introduction of any prior information. When introducing the polarization decay as prior knowledge, a significant improvement was achieved in the lung region, the root mean square value decreased by 45% and from the whole image by 36%. When introducing the mutual anatomical information as prior knowledge, the root mean square decreased by 21% over the lung region and by 15% over the whole image.

Force and vibration generated in apical direction by three endodontic files of different kinematics during simulated canal preparation: An in vitro analytical study.

Three-Dimensional Quantitative Comparative Analysis of Trapezial-Metacarpal Joint Surface Curvatures in Human Populations

The aim of the present research is to calculate the Relative Accuracy (R.A) and Root Mean Square Error (RMSE) for the location of Technical Institute, Mosul in Nineveh Governorate, Iraq. at the northern part of Mosul city by using surveying Instruments (GPS 1230 , Total Station 06 & Level NAK2), to calculate the coordinates and elevations of (16) Ground Control Points which covered the study area. The field data, remote sensing techniques and GIS software (Arc Map GIS10.3) are used to check the digital map of study area that helped the administrator to take the correct decision, determining positions of the future expansionist for buildings, roads, measuring lengths, areas and there coordinates, directions as well as the total costs estimation needed for any development from the final map. The gradient percentage between the highest and lowest points is calculated to be (9.954%). Relative accuracy for the based measured points (R.A) = 1:60000), and Root Mean Square error in Easting coordinates (RMSE) = ± 0.102m, in Northing coordinates (RMSN) = ± 0.096m, the Root Mean Square for the resultant (RMSR) = ± 0.099m, and Root Mean Square for Elevations ( RMSRL)= ± 0.005m. We Matched and correlated (10) measured points from study area with their graphic data positions on the aerial photo, determining the offsets for position and elevations as follows: (RMSE = ± 0.076m), (RMSN = ± 0.125m), (RMSR = ± 0.088m), and (Root Mean Square for Elevations = RMSRL= ± 0.045m). This research enable us after checking the results to produce new maps from Aerial photograph or Digital Image to use it for land uses and future extensions in whole study area.

Radar antennas in the open air are affected by dynamic wind loading during azimuthal scanning. In this state, the acquisition and prediction of the aerodynamic load is the focus of the structure design for the antenna. We performed wind tunnel force tests on flat plate antennas with different aspect ratios. The changes in mean, maximum, and root mean square values of the aerodynamic coefficients relative to the antenna aspect ratio and reduced frequency are given for the first time. The effects of the antenna aspect ratio and reduced frequency on aerodynamic characteristics are analyzed. The experimental results indicate that the magnitude of the azimuthal moment is related to the antenna aspect ratio and the reduced frequency. It is worth noting that the antenna aspect ratio has a significant impact on the mean, maximum, and root mean square values of dynamic aerodynamic coefficients. The mean, maximum, and root mean square values of the rolling moment coefficient, azimuth moment coefficient, and pitching moment coefficient monotonously decrease with the increase in aspect ratio. In addition, the influence of reduced frequency on the dynamic aerodynamic coefficient is closely related to the antenna aspect ratio. Under the same antenna aspect ratio, increasing the reduced frequency will increase the mean, maximum, and root mean square values of the aerodynamic coefficient. For flat plate antennas with different aspect ratios, at the condition of increasing the aspect ratios, the mean, maximum, and root mean square values of aerodynamic coefficients do not change significantly with the change of reduced frequency.