How to Design Imaging Systems Using Mutual Information Estimation

Introduction

Imaging systems—from smartphone cameras to MRI scanners—often produce measurements that are never directly seen by humans; instead, they are processed by algorithms or AI. The true value of these measurements lies not in how they look, but in how much useful information they contain for distinguishing objects. Traditional metrics like resolution or signal-to-noise ratio (SNR) assess isolated aspects of quality, making it hard to compare systems that trade off between factors. Training neural networks for reconstruction or classification conflates hardware quality with algorithm performance. Our approach, detailed in our NeurIPS 2025 paper, uses a direct information-theoretic metric—mutual information—to evaluate and optimize imaging systems. This guide provides a step-by-step method to apply information-driven design to your own imaging system.

What You Need

• Imaging system model: Description of the encoder (optical system) that maps objects to noiseless images (e.g., lens, sensor, sampling scheme).
• Noisy measurement data: Actual or simulated measurements from the system (can be raw sensor data, frequency-space data, etc.).
• Noise model: Statistical model of the corrupting noise (e.g., Gaussian, Poisson, or a known real-world noise profile).
• Information estimator algorithm: Code that estimates mutual information using only the noisy measurements and noise model (e.g., a neural network-based estimator like MINE or our custom method).
• Computational resources: Sufficient memory and compute (GPU recommended) for estimating high-dimensional mutual information.
• Design parameters: Adjustable variables of the imaging system (e.g., aperture size, exposure time, pixel size, sampling pattern) that you wish to optimize.

Step-by-Step Guide

Step 1: Model Your Imaging System as an Encoder

Every imaging system can be viewed as an encoder that maps a physical object (e.g., a scene, an anatomical structure) into a noiseless image. This mapping includes all optical and sampling transformations. Write down the forward model: object → noiseless image. For example, in a simple camera this includes blur from the lens, demosaicing, and quantization. In MRI, it includes the Fourier encoding matrix. Ensure this model captures all deterministic transformations before noise is added.

Step 2: Collect or Simulate Noisy Measurements

Obtain a set of noisy measurements from your system. If you have access to real raw data (e.g., raw sensor files from a phone, k-space data from an MRI), use that. Otherwise, simulate measurements by applying your encoder to known objects and adding realistic noise. The measurements will be your only source of information—avoid using clean images directly in later steps.

Step 3: Establish a Noise Model

Identify the dominant noise sources in your system. For most electronic sensors, this is a combination of photon shot noise (Poisson) and read noise (Gaussian). For MRI, noise is typically Gaussian in the complex domain. Your noise model should be probabilistic: p(measurement | noiseless image). This model is critical because the information estimator uses it to distinguish signal from noise.

Step 4: Implement an Information Estimator

Use an algorithm that estimates the mutual information I(Object; Measurements) from the noisy measurements and the noise model. Avoid methods that require explicit modeling of the object distribution (which is often unknown). Instead, follow our approach: the estimator uses only the noisy measurements and the known noise model to quantify how well the measurements distinguish different objects. For high-dimensional data, a neural network-based discriminator (e.g., MINE) works well. Ensure the estimator is trained or calibrated on the measurement set.

Step 5: Compute Mutual Information for Your Current Design

With the estimator ready, compute the mutual information between the object space (or a set of representative objects) and the measurements. The result is a single number that captures the combined effect of resolution, noise, sampling, and all other factors. A higher value means the measurements contain more useful information for distinguishing objects. This step gives you a baseline for your current system design.

Step 6: Evaluate System Performance Against Traditional Metrics

Compare the mutual information value with traditional metrics like resolution, SNR, or task-specific accuracy. You will likely find that systems with similar mutual information can produce wildly different-looking measurements, yet perform equivalently in downstream tasks (e.g., classification by an AI). This step validates that mutual information is a unifying metric—it accounts for trade-offs that other metrics miss.

Step 7: Optimize Design Parameters to Maximize Mutual Information

Now treat mutual information as your objective function. Use gradient-based or derivative-free optimization to adjust design parameters (e.g., aperture, exposure, pixel size, or encoding pattern). Because the estimator provides a differentiable proxy (if you use neural network-based estimator), you can backpropagate through the imaging system model. This optimization requires only the noisy measurements and noise model—no task-specific decoder training. Our results show that this approach matches state-of-the-art end-to-end methods but with lower memory and compute requirements.

Tips for Success

• Start with simulations: Before applying to real hardware, test the entire pipeline with simulated data where ground-truth information is known. This helps validate your estimator and optimization.
• Mind the dimensionality: High-dimensional mutual information estimation can be unstable. Use techniques like data subsampling, dimensionality reduction (PCA), or ensemble estimators to improve robustness.
• Compare multiple noise models: If you are unsure about the noise distribution, run the estimation with several plausible models. The relative ranking of designs often holds even if the absolute information values shift.
• Leverage domain knowledge: The optimization can be guided by known physics (e.g., diffraction limits, sensor saturation). This speeds up convergence and prevents unrealistic designs.
• Use the right tool: Our NeurIPS 2025 paper provides code and examples for four imaging domains (microscopy, photography, MRI, LiDAR). Check the supplementary materials for implementation details.
• Interpret mutual information wisely: Mutual information tells you how much information is theoretically available. Actual task performance may be lower if your downstream AI cannot extract all of it. Still, maximizing mutual information guarantees that any remaining gap is due to the algorithm, not the sensor.

By following these steps, you can directly evaluate and optimize your imaging system's information capacity, leading to designs that are both efficient and effective for AI-based interpretation.