  In this tutorial, we combine the different scientific fields of information
theory, thermodynamics, regularization theory and non-destructive imaging,
especially for photoacoustic and photothermal imaging. The goal is to get a
better understanding of how information gaining for subsurface imaging works
and how the spatial resolution limit can be overcome by using additional
information. Here, the resolution limit in photoacoustic and photothermal
imaging is derived from the irreversibility of attenuation of the pressure wave
and of heat diffusion during propagation of the signals from the imaged
subsurface structures to the sample surface, respectively. The acoustic or
temperature signals are converted into so-called virtual waves, which are their
reversible counterparts and which can be used for image reconstruction by
well-known ultrasound reconstruction methods. The conversion into virtual waves
is an ill-posed inverse problem which needs regularization. The reason for that
is the information loss during signal propagation to the sample surface, which
turns out to be equal to the entropy production. As the entropy production from
acoustic attenuation is usually small compared to the entropy production from
heat diffusion, the spatial resolution in acoustic imaging is higher than in
thermal imaging. Therefore, it is especially necessary to overcome this
resolution limit for thermographic imaging by using additional information.
Incorporating sparsity and non-negativity in iterative regularization methods
gives a significant resolution enhancement, which was experimentally
demonstrated by one-dimensional imaging of thin layers with varying depth or by
three-dimensional imaging, either from a single detection plane or from three
perpendicular detection planes on the surface of a sample cube.
