† Corresponding author. E-mail:
Project supported by Guangdong Provincial Science and Technology Plan Project of China (Grant Nos. 2015B010114007 and 2014B050505020).
An improved method of using a selective spatial-domain mask to reduce speckle noise in digital holography is proposed. The sub-holograms are obtained from the original hologram filtered by the binary masks including a shifting aperture for being reconstructed. Normally, the speckle patterns of these sub-reconstructed images are different. The speckle intensity of the final reconstructed image is suppressed by averaging the favorable sub-reconstructed images which are selected based on the most optimal pixel intensity sub-range in the sub-holograms. Compared with the conventional spatial-domain mask method, the proposed method not only reduces the speckle noise more effectively with fewer sub-reconstructed images, but also reduces the redundant information used in the reconstruction process.
Compared with the traditional holography, digital holography has many distinct advantages, such as higher imaging speed.[1] Most importantly, the quality of the reconstructed image can be improved by the digital image processing technology. Recently, digital holography is widely applied to particle tracking,[2] deformation measurement,[3,4] holographic microscopy,[5,6] biological cell monitoring,[7] ultrafast recording,[8] and so on. However, the speckle noise seriously affects the signal-to-noise ratio and spatial resolution of the reconstructed image,[9] and limits the application of digital holography. Several effective methods have been proposed to reduce the speckle intensity and its size. For example, Uzan et al. proposed a non-local mean filter method that could reduce the speckle intensity by weighted averaging the intensity of a reconstructed image, but the measure of similarity lacks robustness.[10] Massig et al. proposed a synthetic aperture digital holography to reduce the speckle size, but it required to record multiple holograms, which was not suitable for real-time processing.[11,12]
Maycock et al. proposed a discrete Fourier transform method to obtain multiple reconstructed images with different speckle noise patterns by moving the band-pass filter. However, this method cannot get enough different speckle patterns.[13] Fukuoka et al. proposed a spatial domain mask (SDM) method to reduce the speckle intensity and improve the spatial resolution of the reconstructed image.[14,15] The original hologram was filtered by the binary masks including a shifting aperture, then these sub-holograms were reconstructed. The speckle intensity can be reduced effectively by averaging all the sub-reconstructed images. However, it is obvious that averaging all the sub-reconstructed images without any selective standard is not the best strategy in this method. Therefore, an improved method is proposed in this paper, which can better reduce speckle intensity with fewer sub-reconstructed images.
As shown in Fig.
The procedure of SDM method is performed in Fig.
The improved reconstructed image base on SDM method is given by
The total number of pixels in the original hologram is Nx × Ny. All of the sub-holograms have the same size as that of the original hologram, but the total number of the meaningful pixels in the sub-hologram is equal to the size of the aperture, i.e., Dx × Dy.
The total number of the sub-hologram is given by
In the SDM method, all of the sub-reconstructed images are accumulated without any selective standard, leading to the redundant information in the final reconstructed image and the quality of the image is not good enough.
Based on the deficiencies of the SDM method described above, we propose a selective SDM method. Compared to the original method, the proposed method adds a process of selecting favorable sub-reconstructed images.
According to the theory of digital holography, it is known that each pixel on the hologram has recorded all the information of the object. Therefore, the intensity of each pixel is closely related to the quality of the reconstructed image, and there may be a certain number of pixels within a specific range of intensity values, which are most related to the quality of sub-reconstructed image. The following analysis illustrates this point. This specific range is defined as the optimal pixel intensity range. For different objects or experimental environments, the optimal pixel intensity ranges on the hologram will be different.
The range of pixel intensity values in the hologram recorded by CCD is [0, 255]. In this process, our aim is to select the most optimal pixel intensity sub-range in [0, 255]. In order to select the optimal pixel intensity sub-range, we divide the range into multiple small sub-ranges first, such as
We assume that P[m,n] is the proportion of the pixels whose intensity value is in the sub-range [Im,In] in the total pixels (Dx × Dy), and it is given by
![](cpb_27_10_104202/cpb_27_10_104202_ieqn1.gif)
![](cpb_27_10_104202/cpb_27_10_104202_ieqn2.gif)
![](cpb_27_10_104202/cpb_27_10_104202_ieqn3.gif)
The correlation coefficient between ENL and P[m,n] is given by
If ρ(ENL, P[i,j]) = max ρ(ENL, P[0,a]), ρ(ENL, P[a,b]),…, ρ(ENL, P[x,255]), it is shown that the change in the total amount of pixels whose intensity value is within the range [Ii,Ij] is most relevant to the change in the quality of sub-reconstructed image. So, the pixel intensity sub-range [Ii,Ij] is the most optimal pixel intensity sub-range. The sub-reconstructed images with a high value of P[i,j] are the preferred sub-reconstructed images.
The experimental setup is shown in Fig.
The reconstructed images without any speckle reduction method are shown in Fig.
![]() | Fig. 4. The reconstructed images without any noise reduction. (a) The object is dice; (b) the object is coin. |
During the experiment, based on the two improved methods, the size of the aperture is chosen as 480 × 640, 240 × 320, and 120 × 160, and the shifting interval is 20 pixels by rows or columns. 1500 sub-holograms are selected randomly.
Firstly, we divide the range [0, 255] into these small ranges as [0,50], [50,100], [100, 150], [150, 200], and [200, 255]. The distributions of ENL and P[0,50]−P[200,255] are shown in Fig.
The correlation coefficient between ENL and P[m,n] is given by Eq. (
It is obviously that ρ (ENL, P[0,50]) > ρ (ENL, P[50,100]) > ρ (ENL, P[200,255]) > ρ (ENL, P[150,200]) > ρ (ENL, P[100,150]).
So, we choose the sub-range of [0,50] in the case of dice.
From the ENL and P[0,50]−P[200,255] in Fig.
So, we choose the sub-range of [100,150] in the case of coin. Then we divide the sub-ranges of [0,50] and [100,150] into smaller sub-range respectively as [0,10], [10,20], [20,30], [30,40], [40,50] and [100,110], [110, 120], [120, 130], [130, 140], [140, 150].
The distributions of ENL and P[0,10]−P[40,50] in the case of dice are shown in Fig.
In the case of dice, from the ENL and P[0,10]−P[40,50] in Fig.
So, we choose the sub-range of [20, 30] in the case of dice. And in the case of coin, from the ENL and P[100,110]−P[140,150] in Fig.
So, we choose the sub-range of [100,110] in the case of coin.
Finally, we sort the sub-reconstructed images following the order of P[20,30] or P[100,110], corresponding to dice and coin from the maximum value to the minimum value. And then, we accumulate the sub-reconstructed images in order. The ENL of the final reconstructed image varying with the sequence number of the sub-reconstructed images is shown in Fig.
As revealed in Fig.
![]() | Table 1. The largest ENL and the corresponding number of sub-reconstructed images. . |
As revealed in Table
![]() | Fig. 8. Final reconstructed images using dice and coin. (A1)–(A3): proposed method; (a1)–(a3): SDM method; (B1)–(B3): proposed method; (b1)–(b3): SDM method. |
Comparing Fig.
The highest value of P[20,30] and P[100,110] in all of sub-holograms is shown in Table
![]() | Table 2. The highest value of P[20,30] and P[100,110] in three kinds of apertures. . |
In order to compare the proposed method and SDM method more clearly, we analyze the final reconstructed images from two aspects of edge preservation index (EPI) and the intensity distribution of the pixels.
The EPI indicates the lateral or vertical edge holding ability after image processing.[16] It is given as
![]() | Table 3. The values of ESDM and Eproposed. . |
From Table
In Fig.
In order to reduce the speckle intensity of reconstructed images, the conventional SDM method averages all sub-images and obtains a reconstructed image with weak speckle intensity. However, when the number of sub-images is huge, the reconstructed image will blur the border due to excessive redundant information. An improved method is proposed to deal with this problem well. In this method, the sub-hologram in which the pixel intensity changes gently will be chosen, and then reconstructed as well as averaged to obtain a higher-quality reconstructed image with weaker speckle. The experimental analysis shows that the number of the required sub-images is greatly reduced and the speckle intensity of the reconstructed image is weaker.
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