Eigensensing and deconvolution for the reconstruction of heat absorption profiles from photoacoustic tomography data

Photoacoustic tomography (PAT) is a relatively recent imaging modality that is promising for breast cancer detection and breast screening. It combines the high intrinsic contrast of optical radiation with acoustic imaging at submillimeter spatial resolution through the photoacoustic effect of absorption and thermal expansion. However, image reconstruction from boundary measurements of the propagating wave field is still a challenging inverse problem. Here we propose a new theoretical framework, for which we coin the term eigensensing, to recover the heat absorption profile of the tissue. One of the main features of our method is that there is no explicit forward model that needs to be used within a (usually) slow iterative scheme. Instead, the eigensensing principle allow us to computationally obtain several intermediate images that are blurred by known convolution kernels which are chosen as the eigenfunctions of the spatial Laplace operator. The source image can then be reconstructed by a joint deconvolution algorithm that uses the intermediate images as input. Moreover, total variation regularization is added to make the inverse problem well-posed and to favor piecewise-smooth images.