Derivative encoding for parallel magnetic resonance imaging.

Area of Science:

• Magnetic Resonance Imaging (MRI)
• Signal Processing
• Image Reconstruction

Background:

• Multichannel receive coils in MRI generate complex k space signals.
• Image aliasing is a common artifact in accelerated MRI acquisition.
• Existing parallel imaging methods aim to reconstruct images from undersampled data.

Purpose of the Study:

• To establish a linear, shift-invariant relationship between partial derivatives of k space signals from multichannel coils.
• To demonstrate the utility of k space derivatives for artifact removal, specifically image unwrapping.
• To introduce novel methods for parallel imaging reconstruction.

Main Methods:

• Deriving a theorem relating partial derivatives of k space signals across different coils and directions.
• Utilizing the Fourier transform of k space derivatives to identify spatial origins of aliased pixels.
• Validating the k space derivatives theorem using fully sampled phantom and brain images acquired at 3 Tesla with an eight-channel coil.

Main Results:

• K space derivative encoding offers new approaches for parallel imaging in both k space and image domains.
• Noise amplification in sensitivity encoding reconstruction can be mitigated using k space derivative encoding.
• This method reduces noise without assumptions about image characteristics, potentially improving signal-to-noise ratio (SNR).

Conclusions:

• A linear and shift-invariant relationship exists between partial derivatives of k space signals from multichannel coils.
• This relationship can be leveraged for image unwrapping and enhanced parallel imaging reconstruction.
• K space derivative encoding provides a powerful tool for improving MRI image quality and reconstruction.