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Aliasing

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.
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Related Experiment Video

Updated: Oct 18, 2025

Lensless Fluorescent Microscopy on a Chip

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

High-fidelity approximation of grid- and shell-based sampling schemes from undersampled DSI using compressed sensing:

Robert Jones¹, Chiara Maffei¹, Jean Augustinack¹

¹Department of Radiology, Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital & Harvard Medical School, Charlestown, MA 02129, USA.

|September 29, 2021

Summary

Compressed sensing (CS) applied to diffusion spectrum imaging (CS-DSI) reconstructs complex brain microstructural information from undersampled data. This method accurately approximates diffusion MRI data, enabling detailed orientation reconstruction with reduced scan times.

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Area of Science:

Neuroimaging
Diffusion MRI
Compressed Sensing

Background:

Diffusion MRI (dMRI) enables microstructural analysis, with growing interest in the full ensemble average propagator (EAP) for richer feature extraction.
Diffusion Spectrum Imaging (DSI) provides EAP but requires lengthy acquisition times.
Compressed Sensing (CS) techniques aim to reduce DSI acquisition time while preserving data integrity.

Purpose of the Study:

To validate Compressed Sensing DSI (CS-DSI) for reconstructing the EAP and approximating both fully sampled DSI and multi-shell dMRI data.
To evaluate the accuracy of CS-DSI in orientation estimation using post mortem human brain samples compared to polarization-sensitive optical coherence tomography (PSOCT).
To assess the impact of acceleration factors and signal-to-noise ratio (SNR) on CS-DSI reconstruction accuracy.

Main Methods:

Post mortem high-resolution DSI at 9.4T and PSOCT imaging of human brain samples.
Reconstruction of EAP from undersampled q-space data using two dictionary-based, L2-regularized CS-DSI algorithms.
Evaluation of orientation estimates based on angular error and spurious peaks compared to PSOCT ground truth.

Main Results:

CS-DSI with an acceleration factor of R=3 achieved low angular error and minimal spurious peaks in orientation reconstruction.
The CS-DSI approach accurately approximated fully sampled DSI and multi-shell dMRI data with scan times comparable to high angular resolution multi-shell acquisitions.
Reconstruction accuracy was sensitive to the SNR of training data but robust to SNR loss in test data.

Conclusions:

CS-DSI offers a practical approach for acquiring rich microstructural information from dMRI, suitable for orientation reconstruction and microstructural modeling.
This method provides high-fidelity approximations of both DSI and multi-shell data, significantly reducing scan time.
Further development of CS-DSI holds promise for more efficient q-space acceleration techniques in diffusion MRI research.