Separation of Zeros, a Hermite Interpolation Based and a Frame Based Reconstruction Algorithms for Bandlimited Functions

2016 ◽  
Vol 15 (1) ◽  
pp. 21-35
Author(s):  
A. Antony Selvan ◽  
R. Radha
Keyword(s):  
Hermite Interpolation ◽  
Reconstruction Algorithms ◽  
Bandlimited Functions ◽  
Separation Of Zeros

scholarly journals Cardiac magnetic resonance imaging by retrospective gating: mathematical modelling and reconstruction algorithms

1993 ◽  
Vol 4 (3) ◽  
pp. 241-270 ◽  
Author(s):  
J. B. T. M. Roerdink ◽  
M. Zwaan
Keyword(s):  
Magnetic Resonance Imaging ◽  
Hilbert Space ◽  
Magnetic Resonance ◽  
Synthetic Data ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Resonance Imaging ◽  
Bandlimited Functions ◽  
Retrospective Gating ◽  
Odd Degree

This paper is concerned with some mathematical aspects of magnetic resonance imaging (MRI) of the beating human heart. In particular, we investigate the so-called retrospective gating technique which is a non-triggered technique for data acquisition and reconstruction of (approximately) periodically changing organs like the heart. We formulate the reconstruction problem as a moment problem in a Hilbert space and give the solution method. The stability of the solution is investigated and various error estimates are given. The reconstruction method consists of temporal interpolation followed by spatial Fourier inversion. Different choices for the Hilbert space ℋ of interpolating functions are possible. In particular, we study the case where ℋ is (i) the space of bandlimited functions, or (ii) the space of spline functions of odd degree. The theory is applied to reconstructions from synthetic data as well as real MRI data.

Three dimensional deblurring of transmitted-light brightfield micrographs

1993 ◽  
Vol 51 ◽  
pp. 564-565
Author(s):  
Santosh Bhattacharyya
Keyword(s):  
Image Reconstruction ◽  
Three Dimensional ◽  
Transmitted Light ◽  
Reconstruction Algorithms ◽  
3D Image Reconstruction ◽  
Structural Details ◽  
Spread Function ◽  
Early Testing ◽  
Linearized Model ◽  
Image Reconstruction Algorithms

Three dimensional microscopic structures play an important role in the understanding of various biological and physiological phenomena. Structural details of neurons, such as the density, caliber and volumes of dendrites, are important in understanding physiological and pathological functioning of nervous systems. Even so, many of the widely used stains in biology and neurophysiology are absorbing stains, such as horseradish peroxidase (HRP), and yet most of the iterative, constrained 3D optical image reconstruction research has concentrated on fluorescence microscopy. It is clear that iterative, constrained 3D image reconstruction methodologies are needed for transmitted light brightfield (TLB) imaging as well. One of the difficulties in doing so, in the past, has been in determining the point spread function of the system.We have been developing several variations of iterative, constrained image reconstruction algorithms for TLB imaging. Some of our early testing with one of them was reported previously. These algorithms are based on a linearized model of TLB imaging.

X-Ray Nanotomography (XRMT) Tool for Non-Destructive High-Resolution Imaging of ICs

2001 ◽  
Author(s):  
Wenbing Yun ◽  
Steve Wang ◽  
David Scott ◽  
Kenneth W. Nill ◽  
Waleed S. Haddad
Keyword(s):  
High Resolution ◽  
Process Development ◽  
3D Visualization ◽  
Tomographic Reconstruction ◽  
Reconstruction Algorithms ◽  
X Ray ◽  
Visualization Software ◽  
Volumetric Reconstruction ◽  
Resolution Imaging ◽  
Non Destructive

Abstract A high-resolution table-sized x-ray nanotomography (XRMT) tool has been constructed that shows the promise of nondestructively imaging the internal structure of a full IC stack with a spatial resolution better than 100 nm. Such a tool can be used to detect, localize, and characterize buried defects in the IC. By collecting a set of X-ray projections through the full IC (which may include tens of micrometers of silicon substrate and several layers of Cu interconnects) and applying tomographic reconstruction algorithms to these projections, a 3D volumetric reconstruction can be obtained, and analyzed for defects using 3D visualization software. XRMT is a powerful technique that will find use in failure analysis and IC process development, and may facilitate or supplant investigations using SEM, TEM, and FIB tools, which generally require destructive sample preparation and a vacuum environment.

scholarly journals Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

2021 ◽  
Vol 5 (3) ◽  
pp. 83
Author(s):  
Bilgi Görkem Yazgaç ◽  
Mürvet Kırcı
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Frequency Estimation ◽  
Signal Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Instantaneous Frequency Estimation ◽  
Proposed Model ◽  
Fractional Differential ◽  
Instantaneous Frequencies

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

scholarly journals Radiation Dose Reduction in CT Torsion Measurement of the Lower Limb: Introduction of a New Ultra-Low Dose Protocol

Diagnostics ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1209
Author(s):  
Gabriel Keller ◽  
Simon Götz ◽  
Mareen Sarah Kraus ◽  
Leonard Grünwald ◽  
Fabian Springer ◽  
...  
Keyword(s):  
Radiation Dose ◽  
Radiation Exposure ◽  
Lower Limb ◽  
Low Dose ◽  
Body Volume ◽  
Reconstruction Algorithms ◽  
Pelvic Radiograph ◽  
Lower Radiation Dose ◽  
Median Total Dose ◽  
Image Reconstruction Algorithms

This study analyzed the radiation exposure of a new ultra-low dose (ULD) protocol compared to a high-quality (HQ) protocol for CT-torsion measurement of the lower limb. The analyzed patients (n = 60) were examined in the period March to October 2019. In total, 30 consecutive patients were examined with the HQ and 30 consecutive patients with the new ULD protocol comprising automatic tube voltage selection, automatic exposure control, and iterative image reconstruction algorithms. Radiation dose parameters as well as the contrast-to-noise ratio (CNR) and diagnostic confidence (DC; rated by two radiologists) were analyzed and potential predictor variables, such as body mass index and body volume, were assessed. The new ULD protocol resulted in significantly lower radiation dose parameters, with a reduction of the median total dose equivalent to 0.17 mSv in the ULD protocol compared to 4.37 mSv in the HQ protocol (p < 0.001). Both groups showed no significant differences in regard to other parameters (p = 0.344–0.923). CNR was 12.2% lower using the new ULD protocol (p = 0.033). DC was rated best by both readers in every HQ CT and in every ULD CT. The new ULD protocol for CT-torsion measurement of the lower limb resulted in a 96% decrease of radiation exposure down to the level of a single pelvic radiograph while maintaining good image quality.

scholarly journals A Review of Reconstructing Remotely Sensed Land Surface Temperature under Cloudy Conditions

2021 ◽  
Vol 13 (14) ◽  
pp. 2838
Author(s):  
Yaping Mo ◽  
Yongming Xu ◽  
Huijuan Chen ◽  
Shanyou Zhu
Keyword(s):  
Surface Temperature ◽  
Land Surface Temperature ◽  
Land Surface ◽  
Spatial Scales ◽  
Remotely Sensed ◽  
Urban Heat Islands ◽  
Reconstruction Algorithms ◽  
Gap Filling ◽  
Practical Applications ◽  
Data Gaps

Land surface temperature (LST) is an important environmental parameter in climate change, urban heat islands, drought, public health, and other fields. Thermal infrared (TIR) remote sensing is the main method used to obtain LST information over large spatial scales. However, cloud cover results in many data gaps in remotely sensed LST datasets, greatly limiting their practical applications. Many studies have sought to fill these data gaps and reconstruct cloud-free LST datasets over the last few decades. This paper reviews the progress of LST reconstruction research. A bibliometric analysis is conducted to provide a brief overview of the papers published in this field. The existing reconstruction algorithms can be grouped into five categories: spatial gap-filling methods, temporal gap-filling methods, spatiotemporal gap-filling methods, multi-source fusion-based gap-filling methods, and surface energy balance-based gap-filling methods. The principles, advantages, and limitations of these methods are described and discussed. The applications of these methods are also outlined. In addition, the validation of filled LST values’ cloudy pixels is an important concern in LST reconstruction. The different validation methods applied for reconstructed LST datasets are also reviewed herein. Finally, prospects for future developments in LST reconstruction are provided.

Convergence and stability analysis of the half thresholding based few-view CT reconstruction

2020 ◽  
Vol 28 (6) ◽  
pp. 829-847
Author(s):  
Hua Huang ◽  
Chengwu Lu ◽  
Lingli Zhang ◽  
Weiwei Wang
Keyword(s):  
Noise Suppression ◽  
Reconstructed Image ◽  
Reference Image ◽  
Projection Data ◽  
Ct Reconstruction ◽  
Reconstruction Algorithms ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Stability ◽  
Well Posed

AbstractThe projection data obtained using the computed tomography (CT) technique are often incomplete and inconsistent owing to the radiation exposure and practical environment of the CT process, which may lead to a few-view reconstruction problem. Reconstructing an object from few projection views is often an ill-posed inverse problem. To solve such problems, regularization is an effective technique, in which the ill-posed problem is approximated considering a family of neighboring well-posed problems. In this study, we considered the {\ell_{1/2}} regularization to solve such ill-posed problems. Subsequently, the half thresholding algorithm was employed to solve the {\ell_{1/2}} regularization-based problem. The convergence analysis of the proposed method was performed, and the error bound between the reference image and reconstructed image was clarified. Finally, the stability of the proposed method was analyzed. The result of numerical experiments demonstrated that the proposed method can outperform the classical reconstruction algorithms in terms of noise suppression and preserving the details of the reconstructed image.

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