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Related Concept Videos

Computed Tomography01:10

Computed 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...
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Curvilinear Motion: Rectangular Components

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Imaging Studies III: Computed Tomography

DefinitionComputed Tomography (CT) of the genitourinary (GU) tract is a non-invasive imaging modality that utilizes X-rays and computer processing to generate detailed cross-sectional images of the urinary system, encompassing the kidneys, ureters, bladder, and adjacent structures such as the adrenal glands.PurposeCT scans of the GU tract serve several diagnostic and therapeutic purposes, including:Diagnosis of Urinary Tract Diseases: Detects kidney stones, tumors, cysts, and congenital...

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Related Experiment Video

Updated: May 9, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

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Published on: August 30, 2013

Smoothly clipped absolute deviation (SCAD) regularization for compressed sensing MRI using an augmented Lagrangian

Abolfazl Mehranian1, Hamidreza Saligheh Rad, Arman Rahmim

  • 1Division of Nuclear Medicine and Molecular Imaging, Geneva University Hospital, CH-1211 Geneva, Switzerland.

Magnetic Resonance Imaging
|July 30, 2013
PubMed
Summary

A new regularization technique using the smoothly clipped absolute deviation (SCAD) norm enhances compressed sensing (CS) for faster Magnetic Resonance Imaging (MRI). This method reduces aliasing artifacts more effectively than the standard l1 norm, especially at lower sampling rates.

Keywords:
Augmented LagrangianCompressed sensingSmoothly Clipped Absolute Deviation (SCAD)Total variation

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Area of Science:

  • Medical Imaging
  • Signal Processing
  • Optimization

Background:

  • Compressed sensing (CS) accelerates Magnetic Resonance Imaging (MRI) by reconstructing images from undersampled data.
  • Sparsity-promoting regularization is crucial for CS-MRI, leveraging image compressibility in transform domains.
  • Conventional methods often use the l1 norm, which has limitations at very low sampling rates.

Purpose of the Study:

  • Introduce a novel regularization technique based on iterative linearization of the non-convex smoothly clipped absolute deviation (SCAD) norm for CS-MRI.
  • Aim to achieve lower sampling rates than achievable with the conventional l1 norm while approximating l0 norm properties.
  • Enhance the sparsity-promoting capabilities for improved MR image reconstruction.

Main Methods:

  • Formulate CS-MRI reconstruction as an equality-constrained optimization problem.
  • Employ a variable splitting technique and an augmented Lagrangian (AL) method for efficient optimization.
  • Decompose the problem into sub-problems, linearizing the SCAD norm to yield an adaptively weighted soft thresholding rule.

Main Results:

  • The SCAD-based algorithm adaptively assigns lower weights to gradient fields and wavelet coefficients.
  • This adaptive weighting proves more effective in reducing aliasing artifacts caused by k-space undersampling compared to the l1-based method.
  • Phantom and clinical studies demonstrate the superior performance of the SCAD approach.

Conclusions:

  • The proposed SCAD regularization significantly improves upon the performance of l1-based techniques in CS-MRI.
  • It is particularly beneficial at reduced sampling rates, offering better image quality.
  • SCAD regularization presents a promising alternative for specific CS-MRI applications requiring high acceleration factors.