Reconstruction of apertured Fourier Transform Hologram using compressed sensing

Fourier Transform Holography (FTH) encodes object information as the Fourier spectrum in an interference pattern with the help of a reference point source. Hence, a single Fourier transform (FT) operation is capable to provide a complete object from a digitally reconstructed FTH. However, high intensity values in the central region of the FTH demands central blocking due to the limited dynamic range of a detector in a variety of applications. The central blocking causes the loss of frequency content and hence affects the reconstruction result. Still, it can be properly recovered using signal processing techniques such as Compressive Sensing (CS) or Sparse signal processing. This paper investigates the role of CS for centrally blocked FTH using various kind of beam stops and provide a detailed comparison between usual FT reconstruction and technique equipped with CS. We also provide a detail procedure to apply the CS reconstruction in the FTH and compared the results with and without CS. It is established that an object can be recovered from limited size of a recorded hologram with the constraint that object has to be sparse in known basis. Quantitative analysis has been carried out to compare the quality of reconstruction using inverse Fourier transform (IFT) and CS techniques. Quality of reconstruction is assessed by evaluating measures such as the overall visibility, efficiency and PSNR of reconstruction. The finding highlights that the CS reconstruction is better than that of IFT reconstruction. Both simulation and experimental results demonstrate the effectiveness and robustness of the CS-based approach.