Variable Density Signal Sampling for MRI
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Solution Overview
Problem
Current signal sampling techniques in MRI are inefficient due to the need for high sampling rates, leading to long scan times and motion artifacts, especially when trying to reduce sampling points below the Nyquist rate without compromising image quality.
Innovation Solution
A method for determining optimal sampling points using statistical knowledge of the signal, involving eigenvalue decomposition of the autocorrelation matrix and convex optimization to select a subset of dense grid points for efficient signal reconstruction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If uniform sampling at Nyquist rate is employed, then signal reconstruction accuracy is maintained, but scanning time increases and motion artifacts occur
Solution Approach 1:
The patent applies variable density sampling where different regions of the signal are sampled at different rates. Low spatial frequency components are sampled more densely while high spatial frequency components are sampled less densely, optimizing the balance between reconstruction accuracy and scanning time.
Solution Approach 2:
The patent changes the sampling rate parameter from uniform to variable density based on the signal's spectral characteristics. By adjusting the sampling rate dynamically according to the signal content, the system reduces scanning time while maintaining accuracy.
2Loss of time
If sampling rate is reduced below Nyquist rate, then scanning time is reduced, but signal reconstruction accuracy deteriorates
Solution Approach 1:
The patent implements non-uniform sampling density adapted to the signal's frequency content. Regions with lower frequencies receive higher sampling density while high frequency regions receive lower sampling density, allowing accurate reconstruction at reduced overall sampling rates.
Solution Approach 2:
The patent performs preliminary spectral analysis of the signal to identify the distribution of frequency components. This preliminary action enables the system to design an optimal variable density sampling pattern that prioritizes sampling in regions where the signal has significant energy, thereby maintaining reconstruction accuracy at lower sampling rates.
3Measurement precision
If more samples are collected to obtain higher resolution image, then image quality improves, but scan time increases and motion artifacts occur
Solution Approach 1:
The patent applies variable density sampling to k-space, sampling low spatial frequency regions more densely and high spatial frequency regions less densely. This approach achieves high image resolution with fewer total samples, reducing scan time and minimizing motion artifacts.
Solution Approach 2:
The patent performs preliminary spectral characterization of the signal to determine optimal sampling patterns. This preliminary analysis enables the system to select sampling locations that maximize image quality while minimizing the total number of samples required, thereby reducing scan time.
Data Source
AI summary
An optimal sampling pattern for variable density sampling of a continuous signal uses a statistical knowledge of the signal to determine an autocorrelation matrix from which a basis set is identified. Sampling is performed at locations determined from an eigenvector matrix, and the sampled output provides coefficients for the basis set. The reconstructed signal output is a summation of the multiplication of the coefficients and the basis set.