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Related Concept Videos

State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

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Related Experiment Video

Updated: May 21, 2026

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
09:33

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

Spatial transformation of DWI data using non-negative sparse representation.

Pew-Thian Yap, Dinggang Shen

    IEEE Transactions on Medical Imaging
    |June 20, 2012
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel algorithm for transforming diffusion-weighted imaging (DWI) data by decomposing and reconstructing diffusion signal profiles. This method enables direct spatial transformation in signal space, improving micro-structure alignment.

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    Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
    09:33

    Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

    Published on: July 28, 2013

    Diffusion Imaging in the Rat Cervical Spinal Cord
    10:46

    Diffusion Imaging in the Rat Cervical Spinal Cord

    Published on: April 7, 2015

    Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging
    17:06

    Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging

    Published on: November 8, 2012

    Area of Science:

    • Medical Imaging
    • Neuroscience
    • Biophysics

    Background:

    • Diffusion-weighted imaging (DWI) is crucial for non-invasively probing tissue microstructure.
    • Accurate spatial transformation of DWI data is essential for aligning micro-structural features across subjects or time points.
    • Existing methods often struggle with preserving signal integrity during spatial transformations.

    Purpose of the Study:

    • To develop a novel algorithm for transforming and reconstructing diffusion-weighted imaging (DWI) data.
    • To enable precise alignment of micro-structures by directly transforming diffusion signal profiles.
    • To facilitate the application of various diffusion models post-transformation.

    Main Methods:

    • Decomposition of diffusion signal profiles into weighted diffusion basis functions (DBFs) using sparse representation.
    • Independent reorientation of weighted DBFs based on local affine transformations.
    • Recomposition of reoriented DBFs to obtain transformed diffusion signal profiles.
    • Incorporation of a non-negative constraint and explicit modeling of the isotropic diffusion component.

    Main Results:

    • The proposed algorithm successfully transforms and reconstructs DWI data while preserving micro-structural information.
    • The method allows for direct transformation within the signal space, avoiding intermediate representations.
    • The framework effectively handles noise and avoids artifacts by imposing non-negativity and modeling isotropic components.

    Conclusions:

    • The presented algorithm offers a robust and flexible approach for spatial transformation of DWI data.
    • Direct signal-space transformation enhances the accuracy of micro-structure alignment and downstream analysis.
    • This method opens new possibilities for applying diverse diffusion models to transformed DWI data.