Optimized Kaiser–Bessel Window Functions for Computed Tomography

Nilchian, Masih; Ward, John Paul; Vonesch, Cédric; Unser, Michaël

doi:10.1109/tip.2015.2451955

Cited by 25 publications

(30 citation statements)

References 24 publications

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“…Moreover, the x-ray transform of KBWF does not depend on the orientation θ and admits a closed-form expression [29]. It was shown in [28] that a KBWF represents functions very effectively when using specific parameter values (e.g., m = 2, a = 4, and α = 19). Because the density map V is compactly supported, the sequence c[·] ∈ 2 (Z 3 ) can be restricted to a finite number of nonzero coefficients c = (c[k]) k∈Ω3D , where Ω 3D ⊂ Z 3 and N = Ω 3D .…”

Section: B Discretizationmentioning

confidence: 99%

Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM

Zehni

Donati

Soubies

et al. 2020

IEEE Trans. on Image Process.

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Single-particle cryo-electron microscopy (cryo-EM) reconstructs the three-dimensional (3D) structure of biomolecules from a large set of 2D projection images with random and unknown orientations. A crucial step in the single-particle cryo-EM pipeline is 3D refinement, which resolves a highresolution 3D structure from an initial approximate volume by refining the estimation of the orientation of each projection. In this work, we propose a new approach that refines the projection angles on the continuum. We formulate the optimization problem over the density map and the orientations jointly. The density map is updated using the efficient alternating-direction method of multipliers, while the orientations are updated through a semicoordinate-wise gradient descent for which we provide an explicit derivation of the gradient. Our method eliminates the requirement for a fine discretization of the orientation space and does away with the classical but computationally expensive templatematching step. Numerical results demonstrate the feasibility and performance of our approach compared to several baselines.

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Section: B Discretizationmentioning

confidence: 99%

Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM

Zehni

Donati

Soubies

et al. 2020

IEEE Trans. on Image Process.

Self Cite

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“…The Kaiser window can customize a set of adjustable window functions to provide superior performance for multi-tonal detection, especially for harmonic analysis, and its time domain representation can be expressed as [22] …”

Section: Spectral Characteristics Of Nuttall and Kaiser Windowsmentioning

confidence: 99%

A novel power harmonic analysis method based on Nuttall-Kaiser combination window double spectrum interpolated FFT algorithm

Jin

Chen

Flesch

2017

Journal of Electrical Engineering

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Harmonics pose a great threat to safe and economical operation of power grids. Therefore, it is critical to detect harmonic parameters accurately to design harmonic compensation equipment. The fast Fourier transform (FFT) is widely used for electrical popular power harmonics analysis. However, the barrier effect produced by the algorithm itself and spectrum leakage caused by asynchronous sampling often affects the harmonic analysis accuracy. This paper examines a new approach for harmonic analysis based on deducing the modifier formulas of frequency, phase angle, and amplitude, utilizing the Nuttall-Kaiser window double spectrum line interpolation method, which overcomes the shortcomings in traditional FFT harmonic calculations. The proposed approach is verified numerically and experimentally to be accurate and reliable.K e y w o r d s: power system, harmonic analysis, barrier effect, window function, FFT

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“…All simulations were implemented in Matlab (MathWorks, Natick, MA, USA). Two variants of the projection operator were coded to simulate the acquisition process: one using Kaiser-Bessel window functions (KBWF) as discretizing functions and one based on B-splines [21]. This permits the selection of distinct operators for the acquisition and reconstruction tasks, hence reducing the risk of committing an "inverse crime".…”

Section: Simulation Conditionsmentioning

confidence: 99%

Compressed sensing for dose reduction in STEM tomography

Donati

Nilchian

Unser

et al. 2017

2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017)

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We designed a complete acquisition-reconstruction framework to reduce the radiation dosage in 3D scanning transmission electron microscopy (STEM). Projection measurements are acquired by randomly scanning a subset of pixels at every tilt-view (i.e., random-beam STEM or "RB-STEM"). Highquality images are then recovered from the randomly downsampled measurements through a regularized tomographic reconstruction framework. By fulfilling the compressed sensing requirements, the proposed approach improves the reconstruction of heavily-downsampled RB-STEM measurements over the current state-of-the-art technique. This development opens new perspectives in the search for methods permitting lower-dose 3D STEM imaging of electron-sensitive samples without degrading the quality of the reconstructed volume. A Matlab code implementing the proposed reconstruction algorithm has been made available online.

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Optimized Kaiser–Bessel Window Functions for Computed Tomography

Cited by 25 publications

References 24 publications

Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM

Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM

A novel power harmonic analysis method based on Nuttall-Kaiser combination window double spectrum interpolated FFT algorithm

Compressed sensing for dose reduction in STEM tomography

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