Compressive holography algorithm for the objects composed of point sources.

Abstract

A compressive holography algorithm is proposed for the objects composed of point sources in this work. The proposed algorithm is based on Gabor holography, an amazingly simple and effective encoder for compressed sensing. In the proposed algorithm, the three-dimensional sampling space is uniformly divided into a number of grids since the virtual object may appear anywhere in the sampling space. All the grids are mapped into an indication vector, which is sparse in nature considering that the number of grids occupied by the virtual object is far less than that of the whole sampling space. Consequently, the point source model can be represented in a compressed sensing framework. With the increase of the number of grids in the sampling space, the coherence of the sensing matrix gets higher, which does not guarantee a perfect reconstruction of the sparse vector with large probability. In this paper, a new algorithm named fast compact sensing matrix pursuit algorithm is proposed to cope with the high coherence problem, as well as the unknown sparsity. A similar compact sensing matrix with low coherence is constructed based on the original sensing matrix using similarity analysis. In order to tackle unknown sparsity, an orthogonal matching pursuit algorithm is utilized to calculate a rough estimate of the true support set, based on the similar compact sensing matrix and the measurement vector. The simulation and experimental results show that the proposed algorithm can efficiently reconstruct a sequence of 3D objects including a Stanford Bunny with complex shape.