Inverse optical imaging viewed as a backward channel communication problem.

Area of Science:

• Optics
• Information Theory
• Image Reconstruction

Background:

• The inverse problem in optics is crucial for understanding image reconstruction and is linked to the classical concept of resolving power.
• Classical information theory, based on probability, has limitations in addressing complex data like optical images.

Purpose of the Study:

• To reframe the inverse problem in optics as a communication channel problem.
• To evaluate the maximum number of distinguishable messages (M(epsilon)) recoverable from an image, considering noise.
• To compare classical information theory with topological information theory in the context of optical imaging.

Main Methods:

• Modeling the optical system as a communication channel.
• Utilizing Kolmogorov's epsilon-capacity to quantify information transfer.
• Applying concepts from topological information theory, including epsilon-entropy and epsilon-capacity.

Main Results:

• Derived a formula for M(epsilon) approximately 2(Slog(1/epsilon)) for coherent illumination, where S is the Shannon number.
• Demonstrated that epsilon-capacity in inverse optical imaging closely approximates the information content of the object within the image.
• Showcased the utility of topological information theory for evaluating information in compact sets.

Conclusions:

• The inverse problem in optics can be effectively analyzed using communication channel principles.
• Kolmogorov's epsilon-capacity provides a robust measure for information recovery in optical imaging.
• Topological information theory offers a complementary perspective to classical information theory for understanding image reconstruction limits.