[Paper Review] A Blind Deconvolution Technique Based on Projection Onto Convex Sets for Magnetic Particle Imaging

Onur Yorulmaz, Ömer Burak Demirel+4 more|arXiv (Cornell University)|May 21, 2017

Characterization and Applications of Magnetic Nanoparticles42 references3 citations

TL;DR

This paper proposes a blind deconvolution algorithm for magnetic particle imaging (MPI) that leverages the zero-phase property of the MPI point spread function (PSF) and uses Projection Onto Convex Sets (POCS) with ℓ₁-norm regularization to deblur images without requiring prior knowledge of the PSF. The method outperforms conventional deconvolution techniques like Wiener and Lucy-Richardson in simulations and experiments, especially under noise, relaxation effects, and varying nanoparticle types, enabling improved spatial resolution and image quality in x-space MPI reconstruction.

ABSTRACT

Magnetic Particle Imaging (MPI) is an emerging imaging modality that maps the spatial distribution of magnetic nanoparticles. The x-space reconstruction in MPI results in highly blurry images, where the resolution depends on both system parameters and nanoparticle type. Previous techniques to counteract this blurring rely on the knowledge of the imaging point spread function (PSF), which may not be available or may require additional measurements. This work proposes a blind deconvolution algorithm for MPI to recover the precise spatial distribution of nanoparticles. The proposed algorithm exploits the observation that the imaging PSF in MPI has zero phase in Fourier domain. Thus, even though the reconstructed images are highly blurred, phase remains unaltered. We leverage this powerful property to iteratively enforce consistency of phase and bounded l1 energy information, using an orthogonal Projections Onto Convex Sets (POCS) algorithm. To demonstrate the method, comprehensive simulations were performed without and with nanoparticle relaxation effects, and at various noise levels. In addition, imaging experiments were performed on an in-house MPI scanner using a three-vial phantom that contained different nanoparticle types. Image quality was compared with conventional deconvolution methods, Wiener deconvolution and Lucy-Richardson method, which explicitly rely on the knowledge of PSF. Both the simulation results and experimental imaging results show that the proposed blind deconvolution algorithm outperforms the conventional deconvolution methods. Without utilizing the imaging PSF, the proposed algorithm improves image quality and resolution even in the case of different nanoparticle types, while displaying reliable performance against loss of the fundamental harmonic, nanoparticle relaxation effects, and noise.

Motivation & Objective

• To address the lack of PSF knowledge in MPI image deblurring, which limits the use of conventional deconvolution methods.
• To improve image resolution and quality in x-space MPI reconstruction, which suffers from inherent blurring due to system response and limited field-of-view.
• To develop a robust, PSF-free deblurring technique that maintains accuracy under noise, nanoparticle relaxation, and varying particle types.
• To exploit the zero-phase property of the MPI transfer function in the Fourier domain as a key constraint for blind deconvolution.
• To demonstrate the feasibility and superiority of the proposed method over Wiener and Lucy-Richardson deconvolution in both simulated and experimental MPI data.

Proposed method

• The algorithm uses the observation that the MPI point spread function (PSF) has a zero-phase transfer function, meaning its Fourier transform is real and positive.
• It applies an orthogonal POCS algorithm to iteratively enforce two constraints: the phase of the Fourier transform of the image must remain unchanged (zero-phase), and the ℓ₁-norm of the image intensities must be bounded.
• The method leverages the fast Fourier transform (FFT) for efficient transformation between image and Fourier domains, enabling computational efficiency.
• A fast approximate projection onto the ℓ₁ ball is used to enforce sparsity in the image domain, improving noise resilience.
• The algorithm is initialized with the standard x-space reconstructed image to ensure consistent and high-quality convergence.
• The method does not require PSF measurements or calibration scans, making it truly blind and applicable in real-world scenarios with unknown system responses.

Experimental results

Research questions

• RQ1 Can a blind deconvolution method for MPI be developed that does not require prior knowledge of the point spread function (PSF)?
• RQ2 Does the zero-phase property of the MPI transfer function in the Fourier domain enable reliable image deblurring without PSF information?
• RQ3 How does the proposed POCS-based method perform in comparison to Wiener and Lucy-Richardson deconvolution under realistic conditions such as noise and nanoparticle relaxation?
• RQ4 Can the method maintain high image quality and resolution when applied to MPI data with different nanoparticle types and complex tissue structures?
• RQ5 Is the algorithm robust to loss of the fundamental harmonic and to noise in experimental MPI acquisitions?

Key findings

• The proposed blind deconvolution algorithm significantly outperforms Wiener and Lucy-Richardson deconvolution in both simulated and experimental MPI data, even without PSF knowledge.
• The method achieves improved spatial resolution and image quality by enforcing the zero-phase property of the MPI PSF and ℓ₁-norm sparsity in the image domain.
• In simulations, the algorithm maintained high performance under various noise levels and nanoparticle relaxation effects, demonstrating robustness.
• Experimental results on a three-vial phantom with different nanoparticle types confirmed that the method enhances image clarity and resolution without requiring PSF measurements.
• The algorithm showed reliable convergence and consistent results when initialized with the x-space reconstructed image, outperforming random initialization.
• The method remains effective even when the PSF phase is not exactly zero, as long as phase deviations are small in the central Fourier region, indicating tolerance to minor system non-idealities.