Searcharxiv⌕ Search

arXiv subjects

Julian P. Merkofer

Publications and source records attributed to Julian P. Merkofer.

12 recordsLinked to original sources
arXiv2026

Physics-Informed Sylvester Normalizing Flows for Bayesian Inference in Magnetic Resonance Spectroscopy

Magnetic resonance spectroscopy (MRS) is a non-invasive technique to measure the metabolic composition of tissues, offering valuable insights into neurological disorders, tumor detection, and other metabolic dysfunctions. However, accurate metabolite quantification is hindered by challenges such as spectral overlap, low signal-to-noise ratio, and various artifacts. Traditional methods like linear-combination modeling are susceptible to ambiguities and commonly only provide a theoretical lower bound on estimation accuracy in the form of the Cramér-Rao bound. This work introduces a Bayesian inference framework using Sylvester normalizing flows (SNFs) to approximate posterior distributions over metabolite concentrations, enhancing quantification reliability. A physics-based decoder incorporates prior knowledge of MRS signal formation, ensuring realistic distribution representations. We validate the method on simulated 7T proton MRS data, demonstrating accurate metabolite quantification, well-calibrated uncertainties, and insights into parameter correlations and multi-modal distributions.

stat.ML↗
arXiv2026

Learning Array Signal Topologies as Conditional Neural Manifolds

Subspace methods such as multiple signal classification (MUSIC) achieve super-resolution direction of arrival (DoA) estimation by exploiting the orthogonality between the array manifold and the noise subspace of the measurements. Their accuracy therefore depends on the assumed manifold and degrades under model mismatch, while parameters not identifiable from the spatial manifold cannot be recovered. In this work, we propose the conditional neural manifold (CNM), which replaces the fixed manifold with an observation-conditioned mapping from source parameters to steering vectors. An encoder maps the snapshots to a latent scene representation that conditions a zero-initialized neural field over the parameter space. The manifold is learned without steering-vector supervision by shaping the resulting MUSIC landscape. Since the correction acts on the manifold rather than on the estimator, it can be used by other manifold-based methods without modification. The CNM restores resolution under array imperfections, colored noise, correlated sources, and near-field propagation, and resolves the angle-frequency ambiguity inherent to the nominal spatial manifold.

eess.SP↗
arXiv2026

The 2024 MRSI Data Processing and Quantification Challenge Synthetic Dataset

Synthetic data is central to magnetic resonance spectroscopy method development because they provide ground truths for software validation, reproducible benchmarking, and machine- and deep-learning training. In MRSI, synthetic data must capture spatially varying anatomy, field inhomogeneity, nuisance signals, and measurement effects. The 2024 MRSI Data Processing and Quantification Challenge Synthetic Dataset is a simulated 3T brain FID-MRSI resource with ground-truth metabolite maps developed as a controlled testbed for MRSI processing and quantification methods. Subject-specific simulations used anatomical images and field maps from Human Connectome Project subjects. Tissue masks, quantum-mechanically simulated metabolite basis functions, in vivo-derived macromolecular components, Bloch-simulated post-WET residual water, registered in vivo lipid signals, spectral baseline, $B_0$-dependent frequency shifts, Voigt lineshape variations, and complex Gaussian noise were combined in a forward model. Water and lipid signals were synthesized on a high-resolution grid and Fourier-truncated to the final echo-planar spectroscopic imaging grid to model the finite spatial point spread function. This resource has 24 training and 8 testing datasets containing contaminated FID-MRSI data, anatomical images, $B_0$ maps, metadata, and ground-truth metabolite and component signals. Forward-model parameters are documented, including tissue-specific metabolite concentrations and relaxation times, macromolecular amplitude ratios, the water model, noise, and field-inhomogeneity ranges. This synthetic benchmark supports development and comparison of MRSI processing, nuisance-signal removal, and metabolite-quantification methods, while enabling method evaluation. It illustrates how characterized synthetic data can support rigorous evaluation when ground truth is difficult or impossible to obtain.

physics.med-ph↗
arXiv2026

Synthetic Data in MR Spectroscopy: Current Practices, Applications, and Considerations

The use of synthetic data has emerged as an essential tool in Magnetic Resonance Spectroscopy (MRS) research and applications, providing advantages for optimization of acquisition, software validation, deep learning applications, and enhanced reproducibility. Importantly, synthetic data addresses challenges of limited training data availability, particularly for clinical populations, and offers controlled solutions for investigating uncertainties and unexplained variance with in vivo data. This work provides a review and evaluation of current practices in the use and generation of synthetic data within the MRS field. Conducted by the MRS Synthetic Data Working Group under the Code & Data Sharing Committee of the MRS Study Group of the International Society for Magnetic Resonance in Medicine (ISMRM), this manuscript encompasses existing literature, supplemented by collective experience and in-house methodologies.

physics.med-ph↗
arXiv2026

Data-driven Synthesis of Magnetic Resonance Spectroscopy Data using a Variational Autoencoder

The development of deep learning methods for magnetic resonance spectroscopy (MRS) is often hindered by limited availability of large, high-quality training datasets. While physics-based simulations are commonly used to mitigate this limitation, accurately modeling all in-vivo signal components remains challenging. In this work, we propose a data-driven framework for synthesizing in-vivo MRS data using a variational autoencoder (VAE) trained exclusively on measured single-voxel spectroscopy data. The model learns a low-dimensional latent representation of complex-valued spectra and enables generation of new samples through latent-space sampling and interpolation. The generative performance of the proposed approach is evaluated using a comprehensive set of complementary analyses, including reconstruction quality, feature-level similarity using low-dimensional embeddings, application-based signal quality metrics, and metabolite quantification agreement. The results demonstrate that the VAE accurately reconstructs dominant spectral patterns and generates synthetic spectra that occupy the same feature space as in-vivo data. In an example application targeting GABA-edited spectroscopy, augmenting limited subsets of transients with synthetic spectra improves signal quality metrics such as signal-to-noise ratio, linewidth, and shape scores. However, the results also reveal limitations of the generative approach, including under-representation of stochastic noise and reduced accuracy in absolute metabolite quantification, particularly for applications sensitive to concentration estimates. These findings highlight both potential and limitations of data-driven MRS synthesis. Beyond the proposed model, this study introduces a structured evaluation framework for generative MRS methods, emphasizing the importance of application-aware validation when synthetic data are used for downstream analysis.

physics.med-ph↗
arXiv2025

Anomalous Change Point Detection Using Probabilistic Predictive Coding

Change point detection (CPD) and anomaly detection (AD) are essential techniques in various fields to identify abrupt changes or abnormal data instances. However, existing methods are often constrained to univariate data, face scalability challenges with large datasets due to computational demands, and experience reduced performance with high-dimensional or intricate data, as well as hidden anomalies. Furthermore, they often lack interpretability and adaptability to domain-specific knowledge, which limits their versatility across different fields. In this work, we propose a deep learning-based CPD/AD method called Probabilistic Predictive Coding (PPC) that jointly learns to encode sequential data to low-dimensional latent space representations and to predict the subsequent data representations as well as the corresponding prediction uncertainties. The model parameters are optimized with maximum likelihood estimation by comparing these predictions with the true encodings. At the time of application, the true and predicted encodings are used to determine the probability of conformance, an interpretable and meaningful anomaly score. Furthermore, our approach has linear time complexity, scalability issues are prevented, and the method can easily be adjusted to a wide range of data types and intricate applications. We demonstrate the effectiveness and adaptability of our proposed method across synthetic time series experiments, image data, and real-world magnetic resonance spectroscopic imaging data.

stat.ML↗
arXiv2025

Strategies to Minimize Out-of-Distribution Effects in Data-Driven MRS Quantification

This study systematically compared data-driven and model-based strategies for metabolite quantification in magnetic resonance spectroscopy (MRS), focusing on resilience to out-of-distribution (OoD) effects and the balance between accuracy, robustness, and generalizability. A neural network designed for MRS quantification was trained using three distinct strategies: supervised regression, self-supervised learning, and test-time adaptation. These were compared against model-based fitting tools. Experiments combined large-scale simulated data, designed to probe metabolite concentration extrapolation and signal variability, with 1H single-voxel 7T in-vivo human brain spectra. In simulations, supervised learning achieved high accuracy for spectra similar to those in the training distribution, but showed marked degradation when extrapolated beyond the training distribution. Test-time adaptation proved more resilient to OoD effects, while self-supervised learning achieved intermediate performance. In-vivo experiments showed larger variance across the methods (data-driven and model-based) due to domain shift. Across all strategies, overlapping metabolites and baseline variability remained persistent challenges. While strong performance can be achieved by data-driven methods for MRS metabolite quantification, their reliability is contingent on careful consideration of the training distribution and potential OoD effects. When such conditions in the target distribution cannot be anticipated, test-time adaptation strategies ensure consistency between the quantification, the data, and the model, enabling reliable data-driven MRS pipelines.

eess.SP↗
arXiv2024

WAND: Wavelet Analysis-based Neural Decomposition of MRS Signals for Artifact Removal

Accurate quantification of metabolites in magnetic resonance spectroscopy (MRS) is challenged by low signal-to-noise ratio (SNR), overlapping metabolites, and various artifacts. Particularly, unknown and unparameterized baseline effects obscure the quantification of low-concentration metabolites, limiting MRS reliability. This paper introduces wavelet analysis-based neural decomposition (WAND), a novel data-driven method designed to decompose MRS signals into their constituent components: metabolite-specific signals, baseline, and artifacts. WAND takes advantage of the enhanced separability of these components within the wavelet domain. The method employs a neural network, specifically a U-Net architecture, trained to predict masks for wavelet coefficients obtained through the continuous wavelet transform. These masks effectively isolate desired signal components in the wavelet domain, which are then inverse-transformed to obtain separated signals. Notably, an artifact mask is created by inverting the sum of all known signal masks, enabling WAND to capture and remove even unpredictable artifacts. The effectiveness of WAND in achieving accurate decomposition is demonstrated through numerical evaluations using simulated spectra. Furthermore, WAND's artifact removal capabilities significantly enhance the quantification accuracy of linear combination model fitting. The method's robustness is further validated using data from the 2016 MRS Fitting Challenge and in-vivo experiments.

eess.SP↗
arXiv2024

SubspaceNet: Deep Learning-Aided Subspace Methods for DoA Estimation

Direction of arrival (DoA) estimation is a fundamental task in array processing. A popular family of DoA estimation algorithms are subspace methods, which operate by dividing the measurements into distinct signal and noise subspaces. Subspace methods, such as Multiple Signal Classification (MUSIC) and Root-MUSIC, rely on several restrictive assumptions, including narrowband non-coherent sources and fully calibrated arrays, and their performance is considerably degraded when these do not hold. In this work we propose SubspaceNet; a data-driven DoA estimator which learns how to divide the observations into distinguishable subspaces. This is achieved by utilizing a dedicated deep neural network to learn the empirical autocorrelation of the input, by training it as part of the Root-MUSIC method, leveraging the inherent differentiability of this specific DoA estimator, while removing the need to provide a ground-truth decomposable autocorrelation matrix. Once trained, the resulting SubspaceNet serves as a universal surrogate covariance estimator that can be applied in combination with any subspace-based DoA estimation method, allowing its successful application in challenging setups. SubspaceNet is shown to enable various DoA estimation algorithms to cope with coherent sources, wideband signals, low SNR, array mismatches, and limited snapshots, while preserving the interpretability and the suitability of classic subspace methods.

eess.SP↗
arXiv2023

A Review of Machine Learning Applications for the Proton Magnetic Resonance Spectroscopy Workflow

This literature review presents a comprehensive overview of machine learning (ML) applications in proton magnetic resonance spectroscopy (MRS). As the use of ML techniques in MRS continues to grow, this review aims to provide the MRS community with a structured overview of the state-of-the-art methods. Specifically, we examine and summarize studies published between 2017 and 2023 from major journals in the magnetic resonance field. We categorize these studies based on a typical MRS workflow, including data acquisition, processing, analysis, and artificial data generation. Our review reveals that ML in MRS is still in its early stages, with a primary focus on processing and analysis techniques, and less attention given to data acquisition. We also found that many studies use similar model architectures, with little comparison to alternative architectures. Additionally, the generation of artificial data is a crucial topic, with no consistent method for its generation. Furthermore, many studies demonstrate that artificial data suffers from generalization issues when tested on in-vivo data. We also conclude that risks related to ML models should be addressed, particularly for clinical applications. Therefore, output uncertainty measures and model biases are critical to investigate. Nonetheless, the rapid development of ML in MRS and the promising results from the reviewed studies justify further research in this field.

physics.med-ph↗
arXiv2023

DA-MUSIC: Data-Driven DoA Estimation via Deep Augmented MUSIC Algorithm

Direction of arrival (DoA) estimation of multiple signals is pivotal in sensor array signal processing. A popular multi-signal DoA estimation method is the multiple signal classification (MUSIC) algorithm, which enables high-performance super-resolution DoA recovery while being highly applicable in practice. MUSIC is a model-based algorithm, relying on an accurate mathematical description of the relationship between the signals and the measurements and assumptions on the signals themselves (non-coherent, narrowband sources). As such, it is sensitive to model imperfections. In this work we propose to overcome these limitations of MUSIC by augmenting the algorithm with specifically designed neural architectures. Our proposed deep augmented MUSIC (DA-MUSIC) algorithm is thus a hybrid model-based/data-driven DoA estimator, which leverages data to improve performance and robustness while preserving the interpretable flow of the classic method. DA-MUSIC is shown to learn to overcome limitations of the purely model-based method, such as its inability to successfully localize coherent sources as well as estimate the number of coherent signal sources present. We further demonstrate the superior resolution of the DA-MUSIC algorithm in synthetic narrowband and broadband scenarios as well as with real-world data of DoA estimation from seismic signals.

eess.SP↗