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In photoacoustic tomography (PAT) with flat sensor, we routinely encountertwo types of limited data. The first is due to using a finite sensor and isespecially perceptible if the region of interest is large relative to thesensor or located farther away from the sensor. In this paper, we focus on thesecond type caused by a varying sensitivity of the sensor to the incomingwavefront direction which can be modelled as binary i.e. by a cone ofsensitivity. Such visibility conditions result, in the Fourier domain, in arestriction of both the image and the data to a bow-tie, akin to the onecorresponding to the range of the forward operator. The visible wavefrontsetsin image and data domains, are related by the wavefront direction mapping. Weadapt the wedge restricted Curvelet decomposition, we previously proposed forthe representation of the full PAT data, to separate the visible and invisiblewavefronts in the image. We optimally combine fast approximate operators withtailored deep neural network architectures into efficient learnedreconstruction methods which perform reconstruction of the visible coefficientsand the invisible coefficients are learned from a training set of similar data.

On Learning the Invisible in Photoacoustic Tomography with Flat Directionally Sensitive Detector