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Solution of a Complex Least Squares Problem with Constrained Phase.

¹University of California San Diego.

Linear Algebra and Its Applications

|November 16, 2010

Summary

This summary is machine-generated.

A new direct method finds the least squares solution for complex linear equations with a consistent phase, crucial for magnetic resonance imaging applications.

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Area of Science:

Applied mathematics
Image processing
Biomedical engineering

Background:

Complex linear equations commonly yield solutions with independent real and imaginary parts.
Magnetic resonance imaging (MRI) requires solutions where all elements share a uniform phase.
Existing methods may not efficiently address this phase constraint in MRI.

Purpose of the Study:

To develop a direct method for solving phase-constrained least squares problems.
To provide a solution applicable to specific challenges in magnetic resonance imaging.

Main Methods:

Formulation of the phase-constrained least squares problem.
Development of a direct computational approach to find the constrained solution.

Main Results:

The described method yields a least squares solution with a uniform phase for each element.
Demonstration of the method's applicability in magnetic resonance imaging contexts.

Conclusions:

A direct method effectively solves the phase-constrained least squares problem.
This approach is valuable for magnetic resonance imaging reconstruction and analysis.