Active Sampling for MRI-based Sequential Decision Making

1. Problem Statement

Magnetic Resonance Imaging (MRI) is a superior diagnostic tool but is limited in Point-of-Care (PoC) settings due to high costs, complexity, and long acquisition times. While low-field MRI systems offer a portable solution, they suffer from reduced image quality. To address this, researchers have explored active sampling (selecting specific k-space lines dynamically) and direct inference (diagnosing directly from undersampled k-space without full image reconstruction).

However, existing methods typically optimize sampling for a single diagnostic objective (e.g., just disease detection OR severity quantification) or treat multiple objectives independently. This ignores the natural sequential nature of clinical diagnosis: a radiologist first determines if a disease is present, and only if positive, proceeds to quantify its severity. The paper addresses the research gap: Can a single active sampling policy be learned to handle sequential diagnostic tasks (detection followed by severity assessment) efficiently, exploiting correlations between tasks to further reduce sampling requirements?

2. Methodology

The authors propose a novel Multi-Objective Reinforcement Learning (MORL) framework that treats sequential diagnosis as a single scanning session with a dynamic sampling policy.

A. Framework Architecture

The system operates as a closed-loop process (Algorithm 1):

1. Initialization: Starts with a small, randomly sampled subset of k-space lines.
2. Feature Extraction: Two pre-trained classifiers (a Disease Classifier $f_d$ and a Severity Classifier $f_s$) process the current undersampled k-space data.
   • $f_d$ is trained on all data to detect presence/absence.
   • $f_s$ is fine-tuned from $f_d$ using only diseased data to quantify severity.
   • High-level feature maps from both networks are extracted and stacked to form the agent's internal state.
3. Active Sampling Policy: A policy network ($\pi_\phi$) takes these features as input and selects the next k-space line to acquire.
4. Iteration: The new line is added to the k-space mask, predictions are updated, and the process repeats until a sampling budget is met or a confidence threshold is reached.
5. Sequential Logic: If the disease classifier predicts "No Disease," the severity assessment is skipped (reported as "Not Applicable").

B. Multi-Objective Reward with Lexicographic Ordering

The core innovation is a Step-wise Weighting Reward Function that enforces the clinical workflow order:

• Challenge: Simply summing rewards for detection and severity ignores the logical dependency (severity is irrelevant if no disease exists) and the temporal priority (detect first, then quantify).
• Solution: The authors formulate the problem using Lexicographic Ordering. The reward $r_t$ at step $t$ is a weighted sum:
  $$r_t = w_{disease}(t) \cdot r_d(t) + w_{severity}(t) \cdot r_s(t)$$
• Dynamic Weighting: The weights $w(t)$ are adjusted using cosine interpolation over the sampling steps.
  • Early Steps: High weight on disease detection ($w_{disease} \approx 1$).
  • Later Steps: Weight smoothly transitions to severity quantification ($w_{severity} \to 1$).
  • Gating: If the disease prediction is negative, the severity reward is zeroed out, preventing the policy from wasting samples on severity for healthy subjects.

C. Training Strategy

• Policy Gradient: The policy is optimized using a policy gradient method with greedy action selection.
• Parallel Acquisition: During training, the agent samples $q$ candidate lines in parallel to estimate the gradient efficiently, then executes one line during inference.
• Reward Calculation: Rewards are based on the improvement in classification accuracy (reduction in cross-entropy loss) relative to the ground truth.

3. Key Contributions

1. Sequential Active Sampling: Pioneers a framework that performs sequential diagnostic decisions (detection $\to$ severity) within a single MRI scanning session using active k-space sampling.
2. Lexicographic Reward Mechanism: Introduces a step-wise weighting strategy with cosine interpolation that mimics clinical workflows, ensuring the policy prioritizes disease detection before severity quantification.
3. Patient-Level Adaptation: The policy adapts sampling trajectories based on individual patient features extracted from undersampled data, rather than using fixed population-level patterns.
4. Efficiency: Demonstrates that a single policy can outperform or match multiple single-task policies while significantly reducing the total number of k-space lines required.

4. Experimental Results

The framework was evaluated on the fastMRI Knee dataset for two tasks: ACL Sprain Detection and Cartilage Thickness Loss Assessment.

• Performance vs. Baselines:

  • The proposed Weighted Policy achieved diagnostic performance (AUC and Balanced Accuracy) competitive with Fully Sampled (Oracle) baselines using only 10-15% of the k-space data.
  • It outperformed Policy Recon (reconstruction-based) and Policy Classifier (single-task) baselines, particularly in sequential diagnosis tasks.
  • Crucially, the multi-objective policy did not compromise single-task performance; it matched or exceeded single-task policies even when evaluated on individual subtasks.

• Sampling Efficiency:

  • ACL Sprain: The proposed method reached performance plateaus at Step 13 (AUC 0.886), whereas the reconstruction-based baseline required Step 72 (AUC 0.727).
  • Cartilage Loss: Similar significant reductions in required sampling steps were observed.
  • Time Savings: Simulations suggest a reduction in scan time from ~44,000 ms (Policy Recon) to ~16,000 ms (Weighted Policy) for a typical sequence, a critical advantage for PoC.

• Safety and Risk:

  • At 10% sampling, the Disease Miss Rate was 15.73% (vs. 14.04% for Oracle), a negligible increase.
  • Severity Overestimation was significantly reduced (4.89% vs. 20.59% for Oracle), indicating the method is safer against false alarms that lead to unnecessary treatment.

• Ablation Studies:

  • Transition Weight: The cosine interpolation with early transition ($\beta=0.2$) outperformed linear or no-transition strategies, confirming the importance of the sequential reward structure.
  • Classifier Bias: The system is sensitive to biased pre-trained classifiers, highlighting the need for robust reward models.
  • Parallel Samples: $q=8$ provided the best balance between training convergence speed and computational cost.

5. Significance and Impact

• Advancing PoC MRI: By drastically reducing the number of required k-space samples (and thus scan time) while maintaining high diagnostic accuracy, this work makes MRI more viable for portable, low-field, and emergency Point-of-Care applications.
• Clinical Workflow Alignment: Unlike previous "black box" multi-task models, this framework explicitly models the sequential logic of radiologists (detect $\to$ quantify), leading to more efficient data acquisition strategies.
• Direct Inference Paradigm: It reinforces the shift away from image reconstruction toward direct k-space inference, proving that diagnostic decisions can be made with minimal data if the sampling strategy is intelligently optimized.
• Future Hardware: The work serves as a proof-of-concept for closed-loop, real-time MRI scanners that can dynamically adjust acquisition trajectories based on intermediate diagnostic confidence.

In summary, the paper presents a robust MORL framework that successfully bridges the gap between complex multi-step clinical diagnosis and the constraints of rapid, low-cost MRI acquisition, offering a pathway to smarter, faster, and more accessible medical imaging.