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Identifier

000362151

Title

Compressive sensing in magnetic resonance imaging

Alternative Title

Συμπιεστική δειγματοληψία στην απεικόνιση μαγνητικού συντονισμού

Author

Εμμανουηλίδου, Δήμητρα Στέφανου

Thesis advisor

Τσακαλίδης, Παναγιώτης

Abstract

Since the first magnetic nuclear image was produced in 1973, magnetic resonance (MR) imaging has evolved into a clinically indispensable and efeective tool in diagnostic medicine. Over the years, the rapid growth in clinical applications has been accompanied by numerous technological advances in MR imaging (MRI). Much of this evolution has been accomplished through advances in localization techniques and new mechanisms of contrast which have greatly improved image quality. Still, MRI could benefit from approaches for scan time reduction, with benefits for patients and health care economics. The nature of the MRI constitutes a natural fit for Compressive Sensing (CS). Compressive sensing is a novel framework for recovering and reconstructing compressible signals from undersampled data. The theory of CS goes beyond conventional compression schemes where a signal should be sampled first and compressed afterwards, by stating that a successful signal reconstruction can be guaranteed with high probability by solving a convex optimization problem using only a small number of linear combinations of the signal' s values. Successful reconstruction is guaranteed under two assumptions, namely, the signal is sparse or compressible in some basis and the signal measurements are acquired through "random" sampling. The MR modality meets the two assumptions above. Indeed, MR images are either naturally sparse or may be sparsely represented in an appropriate transformed domain. Furthermore, MR acquisition schemes are quite exible and can be explicitly designed in order to incorporate the notion of randomness. In this thesis, we study the performance of three compressive sensing algorithms when applied to magnetic resonance signal modalities. Our goal is to present the basic MRI concepts as incorporated into the theory of CS, in a fashion that is comprehensible to a wide range of readers. All methods use the CS theory to recover the undersampled raw MR data and reconstruct the MR image but they differ in the minimization formulation of the reconstruction schemes they employ. The methods are thoroughly analyzed, compared and evaluated in terms of reconstruction quality, algorithmic complexity, and time consumption. The first method, Smoothed ℓ0 , invokes the theory of CS and uses an ℓ0 approximation to solve the reconstruction problem. It is a very fast technique with low complexity. The two other methods exhibit higher complexity but they are able to achieve better reconstruction results: ℓ1-magic, a commonly used reconstruction algorithm, solves the optimization problem through Newton steps while Sparse MRI uses a non linear gradient descent technique with backtracking. The algorithms presented herein provide a coherent understanding of the secrets and the ideas behind both CS and MRI theories.

Language

English

Subject

Compressive sensing

Magnetic fields

Magnetic resonance imaging

Optimization problem

Sparse signal

Sparsifying transform

Απεικόνιση μαγνητικού συντονισμού

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