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Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

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 sampling...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
Phase Contrast and Differential Interference Contrast Microscopy01:26

Phase Contrast and Differential Interference Contrast Microscopy

Phase-Contrast Microscopes
In-phase-contrast microscopes, interference between light directly passing through a cell and light refracted by cellular components is used to create high-contrast, high-resolution images without staining. It is the oldest and simplest type of microscope that creates an image by altering the wavelengths of light rays passing through the specimen. Altered wavelength paths are created using an annular stop in the condenser. The annular stop produces a hollow cone of...

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Related Experiment Video

Updated: May 12, 2026

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
06:25

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities.

Jose A Rodriguez1, Rui Xu, Chien-Chun Chen

  • 1Department of Biological Chemistry, UCLA-DOE Institute for Genomics and Proteomics, University of California, Los Angeles, California 90095, USA ; Howard Hughes Medical Institute (HHMI), Chevy Chase, Maryland 20815-6789, USA.

Journal of Applied Crystallography
|April 19, 2013
PubMed
Summary
This summary is machine-generated.

Oversampling smoothness (OSS) is a new iterative algorithm for phase retrieval in Coherent Diffraction Imaging (CDI). It improves reconstruction accuracy for noisy data from weakly scattering objects like biological specimens.

Keywords:
X-ray free-electron laserscoherent diffraction imagingimage reconstructionlensless imagingoversamplingphase retrieval

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Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects
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Published on: February 8, 2014

Area of Science:

  • * Coherent Diffraction Imaging (CDI)
  • * Lensless microscopy
  • * Phase retrieval algorithms

Background:

  • * Coherent Diffraction Imaging (CDI) enables high-resolution, lensless microscopy for diverse specimens using various radiation sources.
  • * Reconstructing fine features in weakly scattering objects from noisy data remains a significant challenge in CDI.
  • * Existing algorithms like Hybrid Input-Output (HIO) and Error Reduction (ER) have limitations with noisy datasets.

Purpose of the Study:

  • * To present an effective iterative algorithm, Oversampling Smoothness (OSS), for phase retrieval from noisy diffraction intensities.
  • * To address the challenge of reconstructing fine features in weakly scattering objects, particularly biological specimens.
  • * To improve the accuracy and consistency of CDI reconstructions in the presence of noise.

Main Methods:

  • * Developed the Oversampling Smoothness (OSS) iterative algorithm for phase retrieval.
  • * OSS utilizes correlation information in the region outside the real-space support.
  • * Employs spatial frequency filtering (smoothness constraint) during iterative reconstruction, balancing HIO and ER approaches.

Main Results:

  • * OSS algorithm demonstrated superior performance compared to HIO, ER-HIO, and NR-HIO algorithms.
  • * Consistent improvements in reconstruction accuracy and consistency were observed across all noise levels.
  • * Validated through numerical simulations with Poisson noise and experimental data from a biological cell.

Conclusions:

  • * Oversampling Smoothness (OSS) is an effective algorithm for phase retrieval in Coherent Diffraction Imaging, especially with noisy data.
  • * The algorithm consistently outperforms existing methods in accuracy and reliability for biological specimens.
  • * OSS is expected to be valuable for the growing field of CDI and other applications requiring phase retrieval from noisy Fourier magnitudes.