Numerical reconstruction of holographic microscopy images based on matching pursuits on a pair of domains

We propose a new numerical-reconstruction method of an object image from its digital hologram. The proposed matching pursuit on a pair of domains (MPPD) method employs a spatial-domain basis and its (Fresnel) transform-domain pair. The transform domain basis is used to decompose the hologram, which yields a set of coefficients. Then, these coefficients are used to reconstruct the spatial-domain object image using the predefined spatial basis. We show the robustness of the proposed method against noise on a simulated hologram of spherical particles. By employing spatial-domain gaussian basis and its transform pair, the image of these particles are recovered successfully. The effectiveness of the proposed method is also demonstrated to a real microscopic-hologram of silica gel spherical particles.