methods based on standards of images and video compression (JPEG, MPEG-4, etc.) [ Wallace (1991), .... Multiscale gigapixel photography. Nature 486 ...
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ScienceDirect Physics Procedia 73 (2015) 328 – 332
4th h International Confereence Photon nics and Info formation Optics, O PhIO O 2015, 28-330 January 2015 2
Methodds of com mpressioon of dig gital holograms E.A. Kurbbatova, P.A A. Cheremk khin*, N.N N. Evtikhiev v, V.V. Krrasnov, S.N N. Starikov v National N Researchh Nuclear Univerrsity MEPhI (Mosscow Engineeringg Physics Institutte), Kashirskoye shosse s 31, Moscoow, 115409, Russia
Absttract Speeed up of transmiission of inform mation about 3D D-scenes and reeducing of archiival memory sizze required to sstore it, are important for surveillance sysstems and biom medical applicattions. For solutiion of these tassks, methods of digital hologrram compressio on are c Theey can be divideed into three gro oups: methods bbased on imagees and used. In the paper thhe most popularr methods are considered. o compression sstandards, scalaar methods and vector methodss. Advantages and a drawbacks of the methodss are considered d. video © 2015 20 015The TheAuthors. Authorrs. Published byy Elsevier © Published by Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer--review under rresponsibility of the National Research R Nucleear University MEPhI M (Moscow w Engineering PPhysics Institutte). Peer-review under responsibility of the National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) Keyw words: digital holoography; hologram m compression; scalar s quantizatioon; vector quantizzation; uniform qu uantization; Lloyyd-Max method; kk mean ns.
1. In ntroduction The T digital hollography, as distinct d from the t photograpphy, allows to register inforrmation not onnly on 2D objjects, but also a on 3D sccenes [Picart et al. (2012), Schnars et aal. (2015), Jup ptner et al. (2005), Cherem mkhin et al. (2 2014, J. Ph hys.: Conf. Seer.)]. As a reesult now it is popular ttechnique in different fieelds of scienntific research h: an interrferometry [M Monroy-Ramiirez et al. (2014), ( Hÿtchh et al. (20 008)], microsscopy [Moldeer et al. (2008), Bian nco et al. (2014)], optical and optoelecctronic inform mation processing [Picart et al. (201 2), Kim (20 012)], reconstruction sttatic and dyynamic 2D and a 3D-scenees [Locatelli et al. (201 13), Evtikhieev et al. (2015), mkhin (2014, Proc. P SPIE)], etc. Characterristics of matrrix photo recoorders are dev velop, Riveenson et al. (2013), Cherem thus now the sizee of files of im mages may bee more than teen megabytess [Brady (2012)]. For transsfer of holograaphic 24 Hz) it is neecessary to haave the channeel with capaciity of 2-4 Gbit/sec. videeo with a standdard frequencyy of movies (2 Thiss size is signifficantly more,, than in stand dard communiication channels. Size of teen minutes of holographic video v will be more than 1 terabyte, soo large volumees of archival memory size are required to t store hologrraphic video.
* Corresponding C autthor. Tel.: +7-4999-324-74-03; fax: +7-499-324-74- 03. E-mail E address:PA ACheremkhin@m mephi.ru
1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) doi:10.1016/j.phpro.2015.09.150
E.A. Kurbatova et al. / Physics Procedia 73 (2015) 328 – 332
For speed up of transmission of holograms and reducing of archival memory size required to store it, it is possible to carry out compression of holograms. It is important for: x surveillance systems (security systems, including detecting live people through smoke and flames [Locatelli et al. (2013)]; registration of objects, including florae and faunae of lakes and seas [Watson et al. (2013), Miccio et al. (2014)]); x medical applications (tomography, supervision over a condition of human organs) [Picart et al. (2012)]); x interferometry [Monroy-Ramirez et al. (2014)]; x microscopy (tracking of the movement of microobjects, erythrocytes, plankton; analysis of cellular structures [Molder et al. (2008)]); x metrology [Naydenova (2011), Wyant (2013)] and etc. There are three main classes of methods of compression of digital holograms: x methods based on standards of images and video compression (JPEG, MPEG-4, etc.) [ Wallace (1991), Mallat (2009), Wiegand et al. (2003), Schwarz (2007), Sullivan et al. (2012), Bruylants et al. (2014), Sateesh et al. (2011), Blinder et al. (2013), Nomura et al. (2005)]; x scalar methods (for example, non-uniform logarithmic quantization) [Naughton et al. (2003), Naughton et al. (2002), Lloyd (1982), Max (1960)]; x vector methods (include systems based on learning and neural networks; for example, k-means method) [Jain et al. (1988), Dhillon et al. (2001), Kohonen et al. (2001), Vesanto et al. (2000), Kanungo et al. (2002), Anderson et al. (2006), Bansal et al. (2004), Park et al. (2009), Hou et al. (2014), Xing et al. (2014)]. In this paper the most popular methods of holograms compression are considered. Advantages and disadvantages are discussed. 2. Application of standard methods of images and video compression to digital hologram For compression of digital holograms it is possible to use standard methods of compression of digital images, for example, conversion to the JPEG format [Bruylants et al. (2014), Sateesh et al. (2011), Blinder et al. (2013), Nomura et al. (2005)]. This group of methods is based on statistical parameters of images and features of visual perception by the human eye. It is focused on elimination of surplus information in images by rejection of unnecessary harmonics of spectral representation. However in case of digital holograms these methods are much less applicable. It deals with four factors. First, quality of reconstructed image from the hologram is more important than visual perception of the compressed hologram. Secondly, algorithms of compression of digital images are most applicable for pictures with gradual changes of brightness. But digital holograms are interferential pictures. Generally there are non-gradual changes of brightness in the hologram as the picture period must be less than 2-4 pixels. Thirdly, usually object of hologram has a lot of details. As a result, not taking into account of various spectral components of the hologram leads to much more serious quality loss of the reconstructed image, than in case of compression of standard photographs. Fourthly, usual pictures are directed on registration of amplitude (intensity) of a wave, and holograms are directed on registration not only amplitude, but also even more on registration of a phase of a wave. Therefore for digital holograms algorithms of compression with quality losses (for example, JPEG) are usually not applicable. It is possible to use compression without quality loss (for example, algorithm of LZW), however it allows to reduce size of file of digital hologram usually to 2 times [Bruylants et al. (2014)]. 3. Methods of scalar quantization of digital holograms In scalar quantization methods, each entrance value will be transformed to one quantized output value, without dependence between values of a signal. The most important parameters of scalar quantization are: x quantity of quantization levels,
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x quantization step. The simplest methods of scalar quantization are rounding to the next preset value and uniform quantization [Naughton et al. (2003), Naughton et al. (2002)]. In first case the values accepted by quantized pixels are defined by number of levels of quantization. Process of uniform quantization consists in division of dynamic range into identical intervals. This method is the most applicable if values of brightness of the image are evenly distributed within dynamic range. If a certain area of values prevails, it is expedient to use other methods, as, for example, nonuniform quantization. At non-uniform quantization the scale of quantization isn't linear. The simplest methods of scalar quantization are the fastest and the simplest in realization among the existing compression methods. However at their use the considerable part of high-frequency components of the hologram is lost that leads to loss of quality of the reconstructed images and reducing of value of diffraction efficiency of the hologram. One of the most important methods of scalar quantization is the Lloyd-Max's method: optimum scalar quantization by criterion of a minimum of a mean square mistake [Lloyd (1982), Max (1960)]. Quantization parameters for this method are: density of distribution of counting, number of levels of quantization, accuracy of approach and the maximum number of iterations of algorithm. Among methods of scalar quantization this method returns the best results of quality of the compressed images, but this method is extremely resource-intensive. Quantization by Lloyd-Max's method has to return considerably better results, than uniform quantization at the expense of accounting of non-uniform distribution of values of brightness along a quantization axis. For the most probable values a quantization error and width of level of quantization will be the smallest, for the least probable the greatest. However if amount of gradation is more than 8 the results received by Lloyd-Max's method not much more exceed the results received when using non-uniform quantization. Thus due to complexity of algorithm and a large number of the iterations, which are necessary for compress hologram without loss of quality, speed of quantization considerably decreases. Values of time of calculation exceed the received by method of uniform quantization of hundreds of times. 4. Methods of vector quantization of digital holograms The basic principle of vector quantization consists in creation of a certain set of elements on the basis of the analysis of the entering data [Jain et al. (1988), Dhillon et al. (2001)]. These elements make “the code book” of values, which are in congruence with quantization levels [Kohonen et al. (2001), Vesanto et al. (2000)]. At the created code book index of a code vector uniquely defines a quantized vector. At quantization of image (hologram) the closest value from existing in the code book is compared to each entering value of brightness. Depending on ways of creation of code book and algorithms of search in it the most applicable vector methods of vector quantization differ on the speed and complexity of realization. At vector quantization of images process of a clustering consists in splitting pixels into clusters (groups) in such a way that there are the closest pixels in each cluster. Usually the criterion of similarity of objects is considered difference of input values from a cluster center value. The most popular method of data clustering is dynamic kernels method (k-means method [Kanungo et al. (2002)]). This method directly minimizes a mean square deviation of values of elements belonging to clusters from values of centers of corresponding clusters. Dynamic kernels method is iterative one. Lack of this method is high sensitivity to initial choice of centers of clusters. Advantages of this method are: simplicity of realization, high efficiency and high speed of work. However in comparison with methods considered in this work, method of dynamic kernels is one of the slowest. Also this method is effective only in cases when clusters contain similar amount of objects and are considerably divided among themselves. This method is poorly applicable in case of noisy images. Isolated points of space can significantly influence on calculation of centers of clusters. For reduction of influence of noise and isolated points on basis of k-means method were created methods of medians (k-medians [Anderson et al. (2006), Bansal et al. (2004)]) and median points (medoids; k-medoids method [Park et al. (2009)]), which are similar to method of dynamic kernels. In these methods for definition of centers of clusters instead of means of clusters medians or medoids of clusters are calculated.
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As a rule, results of methods of dynamic kernels, medians and median points are close to each other if all of them are equally applicable to the considered data. These methods are the best among above-mentioned compression methods according to reconstructed images quality point of view [Hou et al. (2014), Xing et al. (2014)]. Thus, as in case of use of Lloyd-Max method, at expense of a large number of iterations their resource intensity extremely increases. A serious disadvantage of described methods of vector quantization, besides low speed of calculation, is their instability. Results of processing of holograms by these methods strongly depend on an initial choice of centers of clusters and their analogs. The choice of central elements of clusters is random and uncontrollable, therefore it is impossible to stabilize methods 5. Conclusion In this paper the most popular methods of compression of digital holograms from three classes of methods are considered: based on standards images and video, scalar and vector quantization. The first group of methods is poorly applicable in case of compression of digital holograms due to considerable losses among informative spectral components of holograms. Among methods of scalar quantization Lloyd-Max's method is the most qualitative method. This method considerably is inferior on speed to the simplest methods of scalar quantization, which possess the poorest quality of reconstruction from considered in this paper. Vector methods possess high quality of reconstruction and extremely low speed. In case of use of methods of vector quantization quality of reconstruction strongly depends on an initial choice of parameters of method. References Anderson, B.J., Gross, D.S., Musicant, D.R., Ritz, A.M., Smith, T.G., Steinberg, L.E., 2006. 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