Photoacoustic Reconstruction Using Sparsity in Curvelet Frame: Image Versus Data Domain

Curvelet frame is of special significance for photoacoustic tomography (PAT) due to its sparsifying and microlocalisation properties. We derive a one-to-one map between wavefront directions in image data spaces PAT which suggests near equivalence the recovery initial pressure from compressed/subsampled measurements when assuming sparsity frame. As latter computationally more tractable, investigation extent this holds conducted paper immediate practical significance. To end we formulate compare DR, two step approach based on complete volume subsampled followed by acoustic inversion, p 0 R , one where (the pressure, ) directly recovered data. Effective representation requires basis defined range forward operator. propose novel wedge-restriction transform enables us construct such basis. Both problems are formulated variational framework. heavily overdetermined, use reweighted l xmlns:xlink="http://www.w3.org/1999/xlink">1 norm penalties enhance solution. The reconstruction problem DR standard compressed sensing problem, solve using an ADMM-type algorithm, SALSA. Subsequently, time reversal as implemented k-Wave Toolbox. aims recover via FISTA, or ADMM addition including non-negativity constraint. discuss relative merits approaches illustrate them 2D simulated 3D real fair rigorous manner.