The P-transform and photoacoustic image reconstruction.

Photoacoustic imaging is a new imaging modality which converts pressure signals received by an array of transducers to a regional distribution of electromagnetic absorption density. This paper presents a rigorous theory for photoacoustic image reconstruction in a concise format. A new type of transform, the P-transform, is proposed, analysed and presented as the main mathematical tool for reconstruction. It is proved that photoacoustic image reconstruction is intrinsically a three-dimensional (3D) procedure. The spatial smear function (SSF) is introduced. To complete photoacoustic image reconstruction an integral equation must be solved, which is replaced by a matrix approach in a discretized space. An example using synthetic data proves the validity of the photoacoustic image reconstruction theory proposed in the paper. The example shows that even the first-order approximation of photoacoustic image reconstruction gives good agreement with reality. It is also seen from the example that the accuracy and noise immunity of the reconstruction procedure depend on the experimental arrangement.