Recovery of partially occluded objects by applying compressive Fresnel holography Academic Article uri icon

abstract

  • A compressive Fresnel holography approach is suggested for the recovery of partially occluded objects. Reconstruc-tion guarantees are analyzed and the effectiveness of the method is demonstrated using simulations and an experi-mental result showing the reconstruction of a partially occluded resolution chart. The reconstruction of partially occluded objects has been a subject of research in recent years. Generally, one wishes to see through a partially occluding plane in order to get a clear image of a specific target object. In the last decades, advancements in digital image sensors and com-putation capabilities have yielded several opportunities to tackle this problem, where most techniques involve the sensing of the scene from different directions [1–4]. By proper synthesis of the captured perspectives, the object is recovered. Synthesizing different object perspectives to reconstruct an object was also adapted to holography [5]. However, each perspective has degraded resolution com-pared with the original hologram, which may impair the overall performance of the method. In this letter we offer a general technique to recover a partially occluded object from its digitally recorded single hologram using the compressive sensing (CS) ap-proach. CS has already gained ground in the realm of holography [6–10]. The CS approach asserts that given the fact that a signal is sparse, or compressible in some (known) transform domain, Ψ, it can be fully recovered by taking only a subset of its measurements, using some sensing operator, which should hold low coherence with the sparsifying operator. Figure 1 depicts our basic setup: a coherently illuminated object field, u in , with wave-length λ, propagates a distance z 1 and hits a partially oc-cluding plane made of opaque and clear or scattering regions, and is given by p…x†. This may be regarded as a subsampling of the object's Fresnel field; hence the motivation of using the compressive Fresnel holography approach. The wavefield than propagates another distance z 2 and interferes with a reference wave on a CCD. The object's field, u ccd …x†, can be extracted using standard techniques, such as filtering out the unwanted diffraction terms [11], and is described by u ccd …x

publication date

  • January 1, 2012