Radu Balan

Understanding the decision of large deep learning models is a critical challenge for building transparent and trustworthy systems. Although the current post hoc explanation methods offer valuable insights into feature importance, they are inherently disconnected from the model training process, limiting their faithfulness and utility. In this work, we introduce a novel differentiable approach to global explainability by design, integrating feature importance estimation directly into model training. Central to our method is the ScoresActivation function, a feature-ranking mechanism embedded within the learning pipeline. This integration enables models to prioritize features according to their contribution to predictive performance in a differentiable and end-to-end trainable manner. Evaluations across benchmark datasets show that our approach yields globally faithful, stable feature rankings aligned with SHAP values and ground-truth feature importance, while maintaining high predictive performance. Moreover, feature scoring is 150 times faster than the classical SHAP method, requiring only 2 seconds during training compared to SHAP's 300 seconds for feature ranking in the same configuration. Our method also improves classification accuracy by 11.24% with 10 features (5 relevant) and 29.33% with 16 features (5 relevant, 11 irrelevant), demonstrating robustness to irrelevant inputs. This work bridges the gap between model accuracy and interpretability, offering a scalable framework for inherently explainable machine learning.

Purpose: Myelin water fraction (MWF) mapping in the central nervous system is a topic of intense research activity. One framework for this requires parameter estimation from a decaying biexponential signal. However, this is often an ill-posed nonlinear problem resulting in unreliable parameter estimates. For linear least-squares (LLS) problems, the ridge regression theorem (RRT) shows that a Tikhonov regularization parameter exists that will reduce mean square error (MSE) in parameter estimates. We present and apply a nonlinear version of the RRT, λ -NL-RR, to MWF mapping. Methods: For simulated and experimental data, we estimated parameter values with conventional nonlinear least-squares (NLLS) and compared these with values obtained from λ -NL-RR, with the regularization parameter value defined by generalized cross validation. We applied regularization only to signals identified as biexponential according to the Bayesian information criterion. Results: Under conditions of modest SNR and closely spaced exponential time constants in which conventional biexponential analysis methods yield particularly inaccurate results, λ -NL-RR decreases MSE by ~10-15%. Conclusion: Regularization of the NLLS parameter estimation problem for the biexponential model decreased MSE for simulated and in vivo MRI brain data. In addition, this work provides a general framework for regularization of a broad class of NLLS problems.

Purpose: Motion-induced magnetic resonance imaging (MRI) artifacts can deteriorate image quality and reduce diagnostic accuracy, but motion by human subjects is inevitable and can even be caused by involuntary physiological movements. Deep-learning-based motion correction methods might provide a solution. However, most studies have been based on directly applying existing models, and the trained models are rarely accessible. Therefore, we aim to develop and evaluate a deep-learning-based method (Motion Correction-Net, or MC-Net) for suppressing motion artifacts in brain MRI scans. Methods: A total of 57 subjects, providing 20,889 slices in four datasets, were used. Furthermore, 3T 3D sagittal magnetization-prepared rapid gradient-echo (MP-RAGE) and 2D axial fluid-attenuated inversion-recovery (FLAIR) sequences were acquired. The MC-Net was derived from a UNet combined with a two-stage multi-loss function. T1-weighted axial brain images contaminated with synthetic motions were used to train the network to remove motion artifacts. Evaluation used simulated T1- and T2-weighted axial, coronal, and sagittal images unseen during training, as well as T1-weighted images with motion artifacts from real scans. The performance indices included the peak-signal-to-noise ratio (PSNR), the structural similarity index measure (SSIM), and visual reading scores from three blinded clinical readers. A one-sided Wilcoxon signed-rank test was used to compare reader scores, with p < 0.05 considered significant. Intraclass correlation coefficients (ICCs) were calculated for inter-rater evaluations. Results: The MC-Net outperformed other methods in terms of PSNR and SSIM for the T1 axial test set. The MC-Net significantly improved the quality of all T1-weighted images for all directions (i.e., the mean SSIM of axial, sagittal, and coronal slices improved from 0.77, 0.64, and 0.71 to 0.92, 0.75, and 0.84; the mean PSNR improved from 26.35, 24.03, and 24.55 to 29.72, 24.40, and 25.37, respectively) and for simulated as well as real motion artifacts, both using quantitative measures and visual scores. However, MC-Net performed poorly for images with untrained T2-weighted contrast because the T2 contrast was unseen during training and is different from T1 contrast. Conclusion: The proposed two-stage multi-loss MC-Net can effectively suppress motion artifacts in brain MRI without compromising image quality. Given the efficiency of MC-Net (with a single-image processing time of ~40 ms), it can potentially be used in clinical settings.

Purpose: To improve the image reconstruction for prospective motion correction (PMC) of simultaneous multislice (SMS) EPI of the brain, an update of receiver phase and resampling of coil sensitivities are proposed and evaluated.Methods: A camera‐based system was used to track head motion (3 translations and 3 rotations) and dynamically update the scan position and orientation. We derived the change in receiver phase associated with a shifted field of view (FOV) and applied it in real‐time to each k‐space line of the EPI readout trains. Second, for the SMS reconstruction, we adapted resampled coil sensitivity profiles reflecting the movement of slices. Single‐shot gradient‐echo SMS‐EPI scans were performed in phantoms and human subjects for validation.Results: Brain SMS‐EPI scans in the presence of motion with PMC and no phase correction for scan plane shift showed noticeable artifacts. These artifacts were visually and quantitatively attenuated when corrections were enabled. Correcting misaligned coil sensitivity maps improved the temporal SNR (tSNR) of time series by 24% (p = 0.0007) for scans with large movements (up to ˜35 mm and 30°). Correcting the receiver phase improved the tSNR of a scan with minimal head movement by 50% from 50 to 75 for a United Kingdom biobank protocol.Conclusion: Reconstruction‐induced motion artifacts in single‐shot SMS‐EPI scans acquired with PMC can be removed by dynamically adjusting the receiver phase of each line across EPI readout trains and updating coil sensitivity profiles during reconstruction. The method may be a valuable tool for SMS‐EPI scans in the presence of subject motion.

The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames is natural in the...