Information-Driven Design of Imaging Systems

Abstract

Most modern imaging systems process the data they capture algorithmically before—or instead of—human viewing. As a result, performance depends not on how interpretable the measurements appear, but how effectively they encode details for algorithmic processing. Information theory provides mathematical tools to analyze this, but developing methods that can handle the complexity of real-world measurements yet remain practical enough for widespread use has proven challenging.

We introduce a data-driven approach for estimating the information content of imaging system measurements. Our framework requires only experimental measurements and noise characterization, with no need for ground truth data. We demonstrate that these information estimates reliably predict system performance across diverse imaging modalities, including color photography, radio astronomy, lensless imaging, and microscopy. To automate the process of designing imaging systems that maximize information capture we introduce an optimization technique called Information-Driven Encoder Analysis Learning (IDEAL). The tools we develop in this work unlock information theory as a powerful, practical tool for analyzing and designing imaging systems across a broad range of applications.

Video

Information Estimation Framework

We model imaging systems (encoders) as functions that transform objects into images, which are then captured with noise by a detector. Using just these noisy measurements and knowledge of the noise characteristics, we can evaluate system quality and guide improvements.

Information measures how well we can distinguish different objects from noisy measurements. When noise increases, multiple objects could have produced the same measurement, making them harder to tell apart and reducing the information content.

To estimate information, we measure the total variability in measurements and subtract out the portion caused by noise.

Mathematically, this can be written as the difference of two entropies:

These quantities depend on two key probability distributions:

For most imaging systems, we know or can measure the noise distribution $\color{#189EE8}{p(\mathbf{y} \mid \mathbf{x})}$. For example, the random arrival times of photons are known to follow a Poisson distribution. This lets us directly calculate $\color{#189EE8}{H(\mathbf{Y} \mid \mathbf{X})}$.

The measurement distribution $\color{#38AD07}{p(\mathbf{y})}$ is trickier - it depends on both the objects and the imaging system itself. We learn this distribution from data by fitting a model $\color{#38AD07}{p_\theta(\mathbf{y})}$ to a dataset of measurements.

Our approach provides an upper bound on the true information content. Since any estimate we compute will be higher than the true value, we can compare different models by choosing the one that gives the lowest estimate.

Applications of Information Estimation

We tested our information estimation framework across diverse imaging applications. Not only did it match traditional evaluation methods, but it did so without requiring complex reconstruction algorithms or ground truth data. Higher-information measurements consistently produced better results across all tasks: reconstructing color photos, imaging black holes with radio telescopes, capturing scenes with lensless cameras, and analyzing cells under a microscope. This validates our framework as a simpler, faster, and more universal approach to evaluating imaging systems.

Automating Information-Driven Design with IDEAL

Information content can do more than evaluate existing systems—it can guide the design of better ones. Our Information-Driven Encoder Analysis Learning (IDEAL) method automatically optimizes imaging system parameters to maximize information capture. Unlike traditional approaches that require training complex image reconstruction algorithms, IDEAL directly optimizes the imaging system using only the measurement information content.

Information-Driven Encoder Analysis Learning (IDEAL)

The video below shows a filter for color photography being optimized to maximize the information captured in its measurements.

BibTeX

@article{pinkard2024universalevaluationdesignimaging,
      title={Universal evaluation and design of imaging systems using information estimation}, 
      author={Henry Pinkard and Leyla Kabuli and Eric Markley and Tiffany Chien and Jiantao Jiao and Laura Waller},
      year={2024},
      eprint={2405.20559},
      archivePrefix={arXiv},
      primaryClass={physics.optics},
      url={https://arxiv.org/abs/2405.20559}, 
}