FSC-loss: A Frequency-domain Structure Consistency Learning Approach for Signal Data Recovery and Reconstruction

TL;DR

The paper tackles the challenge of recovering high-resolution signal matrices (SM) for magnetic particle imaging (MPI) from time-saving low-resolution measurements, with a focus on preserving high-frequency structure. It introduces a frequency-domain structure consistency loss (FSC-loss) coupled with a signal-component embedding strategy (RIM-embedding) and a self-adaptive multi-scale shifted-window (SMSW) Transformer to model global and local signal structure. Evaluations on simulation datasets and Open MPI data show state-of-the-art high-frequency recovery and the ability to reconstruct ${SM}_{HR}$ from downsampled ${SM}_{LR}$ by factors up to 16, achieving substantial speedups (over 60x faster) with minimal $nRMSE$ error ($nRMSE = 0.041$ reported in the abstract). Applications in three in-house MPI systems demonstrate practical gains in acquisition time and image reconstruction quality, underscoring the method's potential for real-world MPI calibration and diagnostics.

Abstract

A core challenge for signal data recovery is to model the distribution of signal matrix (SM) data based on measured low-quality data in biomedical engineering of magnetic particle imaging (MPI). For acquiring the high-resolution (high-quality) SM, the number of meticulous measurements at numerous positions in the field-of-view proves time-consuming (measurement of a 37x37x37 SM takes about 32 hours). To improve reconstructed signal quality and shorten SM measurement time, existing methods explore to generating high-resolution SM based on time-saving measured low-resolution SM (a 9x9x9 SM just takes about 0.5 hours). However, previous methods show poor performance for high-frequency signal recovery in SM. To achieve a high-resolution SM recovery and shorten its acquisition time, we propose a frequency-domain structure consistency loss function and data component embedding strategy to model global and local structural information of SM. We adopt a transformer-based network to evaluate this function and the strategy. We evaluate our methods and state-of-the-art (SOTA) methods on the two simulation datasets and four public measured SMs in Open MPI Data. The results show that our method outperforms the SOTA methods in high-frequency structural signal recovery. Additionally, our method can recover a high-resolution SM with clear high-frequency structure based on a down-sampling factor of 16 less than 15 seconds, which accelerates the acquisition time over 60 times faster than the measurement-based HR SM with the minimum error (nRMSE=0.041). Moreover, our method is applied in our three in-house MPI systems, and boost their performance for signal reconstruction.

Figures (7)

• Figure 1: Overview diagram of our learning approach for ${\text{SM}}_{{\text{HR}}}$ recovery. To shorten the acquisition time of the ${\text{SM}}_{{\text{HR}}}$ (more than 32h) and sharp image reconstruction, we only need to measure a ${\text{SM}}_{{\text{LR}}}$ (part A) and recover the ${\text{SM}}_{{\text{HR}}}$ by applying the method.
• Figure 2: Overview diagram of our signal component RIM-embedding strategy for ${\text{SM}}_{{\text{HR}}}$ recovery.
• Figure 3: Architecture of our proposed network for high-resolution signal matrix (${\text{SM}}_{{\text{HR}}}$) recovery.
• Figure 4: Error maps of different methods for high resolution SM recovery in Open MPI with four times downsampling. K: respective indexes of different frequencies. HR GT: high resolution ground truth. LR: low resolution.
• Figure 5: Error maps of different methods for image reconstruction in Open MPI with four times downsampling. HR GT: high resolution ground truth.