Coefficients Quantization at Off-axis Digital Hologram Wavelet Compression


Digital holographic information is compressed for storage of 2D- or 3D-objects amplitude and phase distributions, fast transmission, analyzing and displaying of these data. In this paper features of application of wavelet transforms for off-axis digital holograms compression are considered. The combined technique based on zero and twin orders elimination, wavelet compression of the amplitude and phase components of obtained Fourier spectrum and further additional compression of wavelet coefficients by thresholding and quantization is analyzed. Numerical experiments on reconstruction of images from the compressed holograms are performed. The comparative analysis of applicability of various wavelets and additional quantization of coefficients is performed. Obtained results demonstrate possibility of 180 and more times compression using iterative and noniterative methods of coefficients quantization and threshold zeroing less 80% of wavelet coefficients.

Keywords: digital holography, hologram compression, wavelets, quantization, thresholding, digital image processing.

[1] Naughton T.J., Frauel Y., Javidi B., Tajahuerce E. Compression of digital holograms for three-dimensional object reconstruction and recognition // Appl. Opt., Vol. 41, Pp. 4124-4132 (2002).

[2] Shortt A.E., Naughton T.J., Javidi B. Compression of digital holograms of threedimensional objects using wavelets // Opt. Express, Vol. 14, Pp. 2625–2630 (2006).

[3] Dufaux F., Xing Y., Pesquet-Popescu B., Schelkens P. Compression of digital holographic data: An overview // Proc. SPIE, Vol.9599, Pp.95990I (2015).

[4] Kurbatova E.A., Cheremkhin P.A., Evtikhiev N.N., Krasnov V.V., Starikov S.N. Methods of Compression of Digital Holograms // Physics Procedia, Vol. 73, Pp. 328–332 (2015).

[5] Seo Y.-H., Choi H.-J., Kim D.-W. 3D scanning-based compression technique for digital hologram video // Signal Process. Image Commun., Vol. 22, Pp. 144-156 (2007).

[6] Senoh T., Wakunami K., Ichihashi Y., Sasaki H., Oi R., Yamamoto K. Multiview image and depth map coding for holographic TV system // Opt. Eng., Vol. 53 (11), Pp. 112302 (2014).

[7] Jaferzadeh K., Gholami S., Moon I. Lossless and lossy compression of quantitative phase images of red blood cells obtained by digital holographic imaging // Appl. Opt., Vol. 55 (36), Pp. 10409-10416 (2016).

[8] Blinder D., Bruylants T., Ottevaere H., Munteanu A., Schelkens P. JPEG 2000-based compression of fringe patterns for digital holographic microscopy // Opt. Eng., Vol. 53 (12), Pp. 123102 (2014).

[9] Naughton T.J., Mc Donald J.B., Javidi B. Efficient compression of fresnel fields for internet transmission of three-dimensional images // App.Opt., Vol. 42 (23), Pp. 4758-4764. 2003).

[10] Shortt A.E., Naughton T.J., Javidi B. Iterative and non-iterative nonuniform quantisation techniques in digital holography // Proc. SPIE, Vol. 6187, Pp. 618719 (2006).

[11] Cheremkhin P.A., Kurbatova E.A. Numerical comparison of scalar and vector methods of digital hologram compression // Proc. SPIE, Vol. 10022, Pp. 1002227 (2016).

[12] Seo Y.-H., Choi H.-J., Kim D.-W. Lossy coding technique for digital holographic signal // Opt. Eng., Vol. 45(6). Pp. 065802 (2006).

[13] Alfalou A., Brosseau C. Optical image compression and encryption methods // Adv. Opt. Photonics, Vol. 1(3), Pp. 589-636 (2009).

[14] Ren. Z., Su P., Ma J. Information content compression and zero-order elimination of computer-generated hologram based on discrete cosine transform // Opt. Rev., Vol. 20 (6), Pp. 469-473 (2013).

[15] Seo Y.-H., Choi H.-J., Kim D.-W. 3D scanning-based compression technique for digital hologram video // Signal Process. Image., Vol. 22(2), Pp. 144-156 (2007).

[16] Darakis E. Soraghan J.J. Use of fresnelets for phase-shifting digital hologram compression // IEEE Trans. Image Process., Vol. 15 (12), Pp. 3804-3811 (2006).

[17] Viswanathan K., Gioia P., Morin L. Wavelet compression of digital holograms: Towards a view-dependent framework // Proc. SPIE, Vol. 8856, Pp. 88561N (2013).

[18] Kurbatova E.A., Cheremkhin P.A., Evtikhiev N.N. Methods of compression of digital holograms, based on 1-level wavelet transform // Journal of Physics: Conference Series, Vol.737, Pp. 012071 (2016).

[19] Cheremkhin P.A., Kurbatova E.A. Compression of digital holograms using 1-level wavelet transforms, thresholding and quantization of wavelet coefficients // Digital Holography and 3D Imaging Conference. OSA Technical Digest Series (Optical Society of America), paper W2A (2017).

[20] Naughton T.J., Javidi B. Compression of encrypted three-dimensional objects using digital holography // Proc. SPIE, Vol. 5827, Pp. 399-409 (2005).

[21] Shortt A.E., Naughton T.J., Javidi B. Combined optimal quantization and lossless coding of digital holograms of three-dimensional objects // Proc. SPIE, Vol. 6392, Pp. 63920A (2006)

[22] Seo Y.-H., Choi H.-J., Kim D.-W. A efficient coding technique of holographic video signal using 3D segment scanning // J. Korea Info. Commun. Soc., Vol. 32 (2C), Pp. 132-140 (2007).

[23] Bettens S., Yan H., Blinder D., et al. Studies on the sparsifying operator in compressive digital holography // Opt. Express, Vol. 25, Pp. 18656-18676 (2017). [24] Gabor D. A new microscopic principle // Nature, Vol. 161, Pp. 777–778 (1948).

[25] Leith E. N., Upatnieks J. Reconstructed wavefronts and communication theory // J. Opt. Soc. Am., Vol. 52, Pp. 1123–1128 (1962).

[26] Cuche E., Marquet P., Depeursinge Ch. Spatial filtering for zero-order and twinimage elimination in digital off-axis holography // Appl. Opt., Vol. 39 (23), Pp. 4070– 4075 (2000).

[27] Cheremkhin P.A., Evtikhiev N.N., Starikov S.N., Krasnov V.V., Porshneva L.A., Rodin V.G. Comparison of methods of suppression of undesired diffraction orders at numerical reconstruction of digital Fresnel holograms // Proc. SPIE, Vol. 9216, Pp. 92161I (2014).

[28] Bruylants T., Blinder D., Ottevaere H., Munteanu A., Schelkens P. Microscopic offaxis holographic image compression with JPEG 2000 // Proc. SPIE. Vol. 9138. Pp. 91380F (2014).

[29] Han C., Wu W., Li M. Encoding and reconstruction of lensless off-axis Fourier hologram based on the theory of compressed sensing // Chin. J. Lasers, Vol. 41 (2), Pp. 0209015 (2014).

[30] Wan M., Muniraj I., Malallah R., Zhao L., Ryle J.P., Rong L., Healy J.J., Wang D., Sheridan J.T. Sparsity based terahertz reflective off-Axis digital holography // Proc. SPIE, Vol. 10233, Pp. 102330T (2017).

[31] Cheremkhin P.A., Kurbatova E.A. Quality of reconstruction of compressed off-axis digital holograms by frequency filtering and wavelets // Appl. Opt., Vol. 57, Issue 1, Pp. A55-A64 (2018).

[32] Torrence C., Compo G.P. A Practical Guide to Wavelet Analysis // Bull. Am. Meteorol. Soc., Vol. 79, Issue 1, Pp. 61-78 (1998).

[33] Daubechies I. The Wavelet Transform, Time-Frequency Localization and Signal Analysis // IEEE Trans. Inf. Theory, Vol. 36, Issue 5, Pp. 961-1005 (1990).

[34] Cheremkhin P.A., Evtikhiev N.N., Krasnov V.V., Kulakov M.N., Kurbatova E.A., Molodtsov D.Yu., Rodin V.G. Demonstration of digital hologram recording and 3Dscenes reconstruction in real-time // Proc. SPIE, Vol. 9889, Pp. 98891M (2016).

[35] Huynh-Thu Q., Ghanbari M. Scope of validity of PSNR in image/video quality assessment // Electron. Lett., Vol. 44 (13), Pp. 800-801 (2008).

[36] Santoso A.J., Nugroho L.E., Suparta G.B., Hidayat R. Compression Ratio and Peak Signal to Noise Ratio in Grayscale Image Compression using Wavelet // International Journal of Computer Science and technology, Vol. 2, Issue 2, Pp. 7-11 (2011).