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Related Concept Videos

Convolution Properties II01:17

Convolution Properties II

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The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
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Convolution Properties I01:20

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Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
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Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
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Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
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Electron Microscope Tomography and Single-particle Reconstruction01:07

Electron Microscope Tomography and Single-particle Reconstruction

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Transmission electron microscopy (TEM) can be used to determine the 3D structure of biological samples with the help of techniques such as electron microscope tomography and single-particle reconstruction. While single-particle reconstruction can examine macromolecules and macromolecular complexes in vitro conditions only, tomography permits the study of cell components or small cells in vivo.
Electron Tomography
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Lewis Acids and Bases

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In 1923, G. N. Lewis proposed a generalized definition of acid-base behavior in which acids and bases are identified by their ability to accept or to donate a pair of electrons and form a coordinate covalent bond.
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Updated: Feb 4, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Infimal convolution-based regularization for SPECT reconstruction.

Jiahan Zhang1, Si Li2, Andrzej Krol3

  • 1Department of Radiation Oncology, Duke University Medical Center, Durham, NC, 27713, USA.

Medical Physics
|October 7, 2018
PubMed
Summary
This summary is machine-generated.

A new infimal convolution of total variation (ICTV) method reduces staircase artifacts and noise in image reconstruction. This technique allows for a 33% radiation dose reduction while maintaining image quality and improving signal-to-noise ratio.

Keywords:
SPECT reconstructionfixed-point proximity methodsinfimal convolutionnoise suppressionpenalized maximum likelihood optimization total variation regularizationstaircase artifact

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Area of Science:

  • Medical imaging
  • Image reconstruction
  • Regularization techniques

Background:

  • Total variation (TV) regularization is effective for noise suppression but introduces staircase artifacts.
  • Developing advanced regularization methods is crucial for improving image quality and reducing radiation dose in medical imaging.

Purpose of the Study:

  • To develop an infimal convolution of the first- and second-order total variation (ICTV) regularization method to reduce staircase artifacts.
  • To assess the noise suppression capabilities of ICTV and its potential for radiation dose reduction.

Main Methods:

  • Introduced the infimal convolution of total variation (ICTV) as a regularization term in penalized maximum likelihood reconstruction.
  • Employed the preconditioned alternating projection algorithm (PAPA) for image reconstruction.
  • Evaluated noise properties and lesion detectability using Monte Carlo simulations, comparing ICTV-PAPA with conventional TV and Gaussian post-filtered EM (GPF-EM) methods.

Main Results:

  • ICTV-PAPA achieved lower background variability and maintained contrast compared to GPF-EM.
  • Images reconstructed with ICTV-PAPA (80,000 counts/view) showed higher channelized Hotelling observer (CHO) signal-to-noise ratio (SNR) than GPF-EM (120,000 counts/view).

Conclusions:

  • ICTV-PAPA effectively avoids staircase artifacts, unlike TV-PAPA, while yielding higher CHO SNR and comparable spatial resolution.
  • Simulation studies suggest a 33% radiation dose reduction is feasible with ICTV-PAPA compared to the clinical standard GPF-EM.