Related Experiment Video
Updated: May 9, 2026
13:44
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
A statistical method for characterizing the noise in nonlinearly reconstructed images from undersampled MR data: the
Mohammad Sabati1, Haidong Peng, M Louis Lauzon
1Department of Radiology, Miller School of Medicine, University of Miami, Miami, FL 33136, USA.
Magnetic Resonance Imaging
|July 31, 2013
Summary
The Projection Onto Convex Sets (POCS) algorithm
Area of Science:
- Medical imaging
- Signal processing
- Computational mathematics
Background:
- The Projection Onto Convex Sets (POCS) algorithm reconstructs high-resolution images from undersampled k-space data.
- Its deterministic properties are known, but noise influence on reconstructed images is unclear.
Purpose of the Study:
- Investigate statistical noise properties in POCS reconstructions.
- Analyze how missing k-space data affects noise distribution.
Main Methods:
- Experimental treatment of POCS statistical properties.
- Investigation of 12 stochastic noise distribution models.
- Analysis of nonlinear point spread functions.
Main Results:
- Noise distribution shifts from Rayleigh to lognormal as missing data increases.
- For small missing data ratios, noise remains Rayleigh distributed.
- POCS-enhanced noise can dominate over POCS-induced artifacts.
Conclusions:
- POCS noise characteristics differ significantly from linear Fourier reconstruction.
- A general statistical method is presented for assessing nonlinear reconstruction noise.
Keywords:
NoiseNonlinear image reconstructionPoint spread functionProjection-onto-convex sets (POCS)Random distributionsSparse samplingStatistical methodsUndersampled acquisitionZero-fillingMore Related Videos
Related Concept Videos
01:18Aliasing
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...
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
01:10Computed Tomography
Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...
01:10Reconstruction 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...
01:22Upsampling
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...