## 1 Background  
Optical scanning holography (OSH) [1; 2] is one of the most effective techniques for capturing a complex hologram of a physical scene. It is different from existing methods such as phase shifting holography (PSH) [3], parallel phase shifting holography (PPSH) [4], geometric phase shifting digital holography (GPSDH) [5], Fresnel incoherent correlation holography (FINCH) [6; 7], Fourier incoherent single channel holography (FISCH) [8], and the consumers scanner approach [9] that requires 2-D digital recording devices (e.g., digital camera) to capture the holographic signal, OSH only utilizes a single-pixel sensor. As such, OSH is a unique holographic recording technique and can even be configured to operate in both coherent and incoherent modes. Operating in the incoherent mode is important as the technique can be used to capture fluorescent specimens holographically. As mentioned in [2], OSH has many applications, such is but not limited to 3-D pattern recognition, 3-D microscopy, 3-D cryptography, and 3-D optical remote sensing. An OSH system can also be implemented to operate at high frame-rate for capturing hologram of a dynamic scene. In general, after a complex hologram is captured, it is often necessary to reconstruct a visible image from the hologram for further inspection and analysis. To reconstruct a hologram, we can back-propagate the hologram onto a sequence of regular spaced reconstruction planes that is parallel to the hologram. If a reconstruction plane is containing object points on the scene, those points will appear as a focused image, otherwise they will take the form of a de-focused haze. The operator or analyst will have to inspect each reconstruction plane, extract the focused image of the object points, if any, and discard the de-focused haze. Although this approach is feasible, the process is time-consuming and the quality of the reconstructed image will be affected by the visual judgment of the operator. For an OSH system that is employed to capture moving objects, it is desirable that the image reconstruction process should not be too lengthy. As such, the algorithms that are used for the reconstruction of optical scanning holograms should be automatic and computationally efficient. Automatic reconstruction of simple binary images from a hologram has been attempted utilizing Weiner filtering [10] and the Wigner distribution [11; 12]. [PERSON] and [PERSON] have proposed a hologram reconstruction method known as \"blind sectional reconstruction\" (BSR) [13; 14]. The method can be divided into 2 stages. First, edge detection is applied to the image in each reconstruction plane. A reconstruction plane that exhibits a local minimum of edge points, as compared with the neighboring planes, will be taken as a focused section containing object points of the scene. This process is sometimes referred to as \"automatic focus detection\" (AFD). Second, a focused image of the object points that are contained in each of the focused section is obtained through an iterative optimization process, while the de-focused haze will be discarded. Subsequently, the focused images in all the sections can be merged to form an overall, focused image of the 3-D object scene with an extended depth of field. Despite the success of the BSR method, the process is computationally intensive, involving a large amount of memory in the optimization process, and so far, only reconstruction of simple binary images has been demonstrated. However, some enhancement of the method has been made to speed up the calculation and lower the memory requirement [15]. A fast variant of the BSR method was adopted in [16]. Similar to the blind sectional reconstruction, a subset of focused sections is obtained from the sequence of reconstructed planes through AFD. Next, simple edge analysis technique is applied to extract the focused object image (and to reject the de-focused haze) in each focused section.