KR20090088053A - Nosie reduction method for digital hologram - Google Patents

Abstract

A noise reduction method of a digital hologram is provided to analyze data after frequency-converting a digital hologram, thereby effectively removing noise. A global DCT(Discrete Cosine Transform) digital hologram is divided into an object area and a background area based on an object outline map. A histogram transform method is applied to the object area. The background area having small correlation with image quality of a restoration image is substituted by 0. The amount of noise spread in the entire image is reduced. Noise occurring during acquisition/transmission processes of the digital hologram is effectively removed.

Description

Noise reduction method for digital hologram {Nosie Reduction Method for digital hologram}

Digital Hologram, Filter Design, Image processing

[Reference 1] Lee Young-hee, “A Study on Digital Contents,” Journal of the Korean Information Science Society, 2004.5 Vol.20-5, pp. 100 ~ 106

[Document 2] Digital, C., "Digital Contents Course-ware," IEEE Multimedia, 2004.7, Vol. Pp. 10-7, 100-110.

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[4] T. J. Naughton, Y. Frauel, B. Javidi and E. Tajahuerce, "Compression of digital holograms for three-dimensional object recognition," SPIE Proc. , 2001, Vol 4471, pp. 280-289.

[5] T. J. Naughton, Y. Frauel, B. Javidi and E. Tajahuerce, "Compression of digital holograms for three-dimensional object reconstruction and recognition," Appl. Opt. 41, 2002.7, No. Pp. 20, 4124-4132.

[6] T. J. Naughton and B. Javidi, "Compression of Encrypted Three-dimensional Objects using Digital Holography," Optical Engineering ,, October 2004. vol. 43, no. 10, pp. 2233-2238

[7] T. J. Naughton, Y. Frauel, E. Tajahuerce, and B. Javidi, "Compression of Digital Holograms for Three-Dimensional Object Reconstruction and Recognition," Applied Optics, July 10, 2002 vol. 41, no. Pp. 20, 4124-4132.

8 T. J. Naughton, J. B. Mc Donald, and B. Javidi, "Efficient compression of Fresnel fields for Internet transmission of three-dimensional images," Applied Optics-Information Processing, August 2003. vol. 42, no. 23, pp. 4758-4764.

[9] Y. H. Seo, H. J. Choi, and D. W. Kim, "Lossy Coding Technique for Digital Holographic Signal", SPIE Optical Enginnering,, 2006.06, vol. 45, no. 6. pp. 5802-1 through 5802-10.

[Reference 10] Choi, Hyun-Joon, Young-Ho Suh, Yoo Sang-Seo, Kim Dong-Wook, "Analysis and Watermarking Techniques of Digital Hologram Using Global 2D DCT", Journal of The Korean Institute of Maritime Communication Sciences, 2007.07, Vol. 11, No. 7,. Pp. 202--207.

[11] J. S. Lee, "Digital Image Smoothing and the Sigma Filter," Computer Graphics and Image Processing, 1983, 255-269.

Document 12 http://www2.edge.no/projects/index.php?expn

   = 2 & target = holovision / abo

The noise of the digital hologram is generated by the environment around the camera and the state of the sensor in the process of acquiring the interference pattern using the CCD camera. Noise deteriorates the quality of the 3D image reconstructed in space and increases the entropy of the original digital hologram, reducing the efficiency of existing digital hologram compression techniques.

In the present invention, an efficient noise reduction technique was developed by analyzing the data after frequency conversion of the digital hologram by introducing DCT.

In the present invention, the frequency conversion is performed by using the global DCT to remove the noise of the digital hologram. We treat the frequency domain as a natural phenomenon and separate it into object domain and background domain.

Experimental results show that the histogram processing method is applied to the object area and the background area is replaced with '0', and the PSNR is improved by more than 6dB.

1. Analysis of Digital Holograms

Digital holograms show quite different characteristics from normal natural images because they record the phase of an object as digital data. In general, natural images show strong correlation between adjacent pixels as well as self-similarity which is the basis of fractal theory. However, digital holograms are abnormal signals with very discontinuous characteristics, such as noise images. An example of such a natural image and a digital hologram is shown in FIG. 1.

As shown in Fig. 1- (d), the digital hologram has different characteristics from natural images. Therefore, it is difficult to expect high effects if the existing noise reduction techniques that have been studied for natural images are applied to digital holograms as they are. Taking into account these characteristics, the team applied DCT to the digital hologram and converted it into the frequency domain.

The reason for introducing DCT in the present invention is that the generation formula of the digital hologram is based on a cosine function, and it is assumed that an image similar to the original object can be obtained when DCT is applied. In FIG. 2, the object image used to generate the digital hologram, the generated digital hologram, and the DCT are shown. DCT used the 256 × 256 global DCT technique for the entire image as in Equation (1).

Here, u and v are coordinates of the frequency conversion region, x and y are coordinates of the original image, and N is the number of pixels to perform the two-dimensional DCT.

2. Noise Reduction Algorithm

2.1. Noise model

Converts the original object image o (x, y) to digital hologram h (i, j) by CGH method and adds N (0, σn2) Gaussian noise to mix the digital hologram h '(i, j) may be defined as in Equation (2) below.

Assume n (i, j) is a white Gaussian noise with a mean of zero. The noise addition model described in Equation (2) is shown in FIG. 3.

2.2. Noise Rejection Algorithm for Digital Hologram

As shown in FIG. 2 (C), when global DCT is performed on a digital hologram, a distribution of coefficients very similar to an object image is observed in a frequency domain. The team attempts to describe a new noise reduction technique assuming the distribution of coefficient values in the frequency domain as natural images.

4 shows the 256 × 256 global DCT results of the original digital hologram and the noise-added digital hologram, and their coefficient distribution.

As shown in Figs. 4 (c) and 4 (d), pixel values in an object observed in the frequency domain have a very low correlation with surrounding pixels and relatively small pixel values are distributed outside the object. To take advantage of the distribution of these pixel values, the team separates objects and backgrounds in the frequency domain and then describes different noise reduction techniques. In FIG. 5, an object contour map generated to separate an object from a background is shown.

The object contour map of FIG. 5 is an image obtained by binarizing an edge region with a target of a global DCT digital hologram and setting a threshold value. In the present invention, the threshold value is set to 200.

In the present invention, after obtaining the object contour map in the frequency domain of the digital hologram, the following four techniques for noise reduction are described.

■ Method 1: Replace background area with '0'

■ Method 2: Replace the background area with '0' and apply the sigma filter to the object area

■ Method 3: Apply the histogram conversion technique to the entire frequency domain

■ Method 4: Separate object and background area and apply histogram conversion method to each

Method 1 separates the global DCT digital hologram into object area and background area based on the object contour map and replaces all background areas with low correlation with the image quality of reconstructed image with '0' to remove noise spread throughout the image. It is a technique to reduce the amount. Method 2 applies a sigma filter that separates the object area from the background area, replaces the background area with '0', and restores the object area to the average of pixels with values similar to the center pixel among the pixels in the filtering window. . The sigma filter is shown in Equation (3) below.

Where R (m, n: i, j) is the noise-reduced pixel value, h '(i, j) is the pixel value of the noise-added digital hologram, and h (m, n) is the peripheral pixel value. Therefore, blurring phenomenon can be reduced when the difference between the center pixel and the surrounding pixel is large like the object region. The threshold Δ is determined using the variance of the predicted noise.

Methods 3 and 4 were applied to noise reduction by analyzing the histogram distribution of coefficients after global DCT of digital hologram. Digital holograms created by applying the CGH method to 100 object images created by computer graphics were used to obtain statistical histogram distribution characteristics. Four representative object images among 100 object images are shown in FIG. 6.

8 shows statistical histogram characteristics of global DCT digital holograms. Global DCT was performed on all 256 × 256 pixels.

In the present invention, the spectrum of noise is estimated by comparing the statistical histogram distribution of coefficients in the frequency domain of the digital hologram. Subsequently, the histogram distribution of the noise region as shown in Fig. 7- (b) is transformed into a distribution similar to the histogram distribution of the original digital hologram as shown in Fig. 7- (a) to restore coefficient values predicted as noise.

Method 3 applies the histogram processing method to the whole image, and Method 4 applies the histogram processing method to the object area and replaces the background area with '0' after separating the object area and the background area. The histogram processing technique is as shown in Equation (4) below.

Where rs [n] is the shifted histogram distribution, hs [n] is the histogram with noise added, c is the weighting factor, and σ is the variance.

 3. Experiment and Discussion

We applied a noisy digital hologram with a Sigma filter and four techniques described by our team. After applying the noise reduction technique, the subjective picture quality and PSNR of 3D holographic images reconstructed by PC simulation were measured.

The experimental environment is as follows.

■ Digital Hologram Size: 256 × 256 [pixel2]

■ SLM pixel size: 10.4㎛ × 10.4㎛

■ Wavelength of light source: 633nm

■ Distance restored: 1,000㎜

(1) The result of applying the existing noise reduction algorithm

The sigma filter, which was used for noise reduction of natural images, was applied to noise reduction of rabbit image digital hologram. Filtering was performed in the hologram region of the noisy digital hologram and the global DCT frequency region, respectively. 9 shows the experimental results.

As shown in FIG. 8, when the noise is removed by the sigma filter used in the natural image, the image quality of the reconstructed image is deteriorated. As a result of measuring PSNR for objective image quality evaluation, the reconstructed image of noise added digital hologram was 24.35dB and the reconstructed image of sigma filter removed 21.53dB. As a result of the experiment, it was confirmed that the image quality of the reconstructed image is deteriorated when the technique developed for the noise reduction of the natural image is applied to the digital hologram as it is.

(2) The result of applying the developed technology

Table 1 shows the noise reduction results using the four techniques described in Section 2.3. Based on the original digital hologram, we show the PSNR values measured by applying noise-added digital hologram and noise cancellation techniques. As can be seen from the table, applying the method 4 resulted in a PSNR improvement of about 6dB or more.

9 shows reconstructed images simulated in a PC for subjective image quality measurement of noise reduction results.

Methods Noisy digital hologram Denoising digital hologram One   24.35 dB 26.55 dB 2 26.75 dB 3 29.63 dB 4 30.47 dB

1-an example of an image; (a) natural image, (b) pixel value distribution diagram (a), (c) digital hologram, (d) pixel value distribution diagram (c)

Figure 2-(a) object image, (b) digital hologram of (a), (c) 256x256 global DCT result of (b).

3-noise model.

Figure 4-(a) DCT result of original digital hologram, (b) DCT result of digital hologram with noise added, (c) pixel value distribution diagram of (a), (d) pixel value distribution diagram of (b).

5-object contour map in the frequency domain.

6-an example of an object image; (a) rabbit, (b) duck, (c) spring, (d) kettle.

7-Statistical histogram distribution in the frequency domain of the digital hologram; (a) Original digital hologram, (b) Noisy digital hologram.

Figure 8-Noise rejection results with sigma filter; Digital hologram (a) Original, (b) Noise added, (c) Noise canceled, Restoration result (d) Original, (e) Noise added, (f) Noise canceled.

Figure 9-Reconstructed images with noise removed (a) Original, (b) Noise added, (c) Method 1, (d) Method 2, (e) Method 3, (f) Method 4.

Claims (2)

Electronic Noise Reduction Techniques for Digital Holograms Noise Reduction Technique Using the Characteristics of Digital Hologram in Frequency Domain

Images