Quality of reconstruction of compressed off-axis digital holograms by frequency filtering and wavelets

Abstract

Compression of digital holograms can significantly help with the storage of objects and data in 2D and 3D form, its transmission, and its reconstruction. Compression of standard images by methods based on wavelets allows high compression ratios (up to 20-50 times) with minimum losses of quality. In the case of digital holograms, application of wavelets directly does not allow high values of compression to be obtained. However, additional preprocessing and postprocessing can afford significant compression of holograms and the acceptable quality of reconstructed images. In this paper application of wavelet transforms for compression of off-axis digital holograms are considered. The combined technique based on zero- and twin-order elimination, wavelet compression of the amplitude and phase components of the obtained Fourier spectrum, and further additional compression of wavelet coefficients by thresholding and quantization is considered. Numerical experiments on reconstruction of images from the compressed holograms are performed. The comparative analysis of applicability of various wavelets and methods of additional compression of wavelet coefficients is performed. Optimum parameters of compression of holograms by the methods can be estimated. Sizes of holographic information were decreased up to 190 times.

Wavelet compression of off-axis digital holograms using real/imaginary and amplitude/phase parts

“…The most popular and fastest noniterative methods are methods of scalar quantization. The majority of quantization resource-intensive iterative methods process one file during a considerable time (tens and hundreds of seconds) with MATLAB using a standard computer 39 . However, the simplest methods of scalar quantization process a hologram during fractions of a millisecond or of a second.…”

“…The previously 39 investigated combined algorithm for hologram compression included the following steps:frequency filtering of unwanted diffraction orders (twin and zero-order images),obtaining an array with A/P parts of the Fourier spectrum of the filtered hologram,performing wavelet decomposition of the separated A/P parts,threshold processing of the wavelet coefficients of A/P parts, andquantizing the thresholded wavelet coefficients of A/P parts.For increasing compression ratios, lossless techniques can be applied for further processing of the quantized thresholded wavelet coefficients.Use of the R/I parts of the Fourier spectrum instead of A/P should provide higher reconstruction quality. The combined algorithm does the following:frequency filtering of the twin and zero-order images,separating the R/I parts of the Fourier spectrum of the filtered hologram,performing wavelet decomposition of the separated R/I parts,threshold processing of the wavelet coefficients of both components, andquantizing the thresholded wavelet coefficients of both components.…”

“…Application of several different wavelets for compression of digital holograms was considered in detail in 51 ; however, results of application of additional processing of decomposition coefficients are not given. Seven different wavelets were used for off-axis hologram compression based on coding of A/P of the filtered spectrum in 39 . However, use of the Fourier spectrum the R/I parts as a more preferable method of compression was not considered.…”

“…Only a few papers have addressed single digital hologram compression and only compression of the amplitude matrix has been considered 53 .For off-axis 54 holograms, undesirable diffraction orders (zero-order and twin images) can be eliminated also 55 . Frequency filtering techniques are often used for reducing the informative holographic data size considerably 39,40 .Currently, off-axis hologram compression is researched for problems in microscopy (images of red blood cells 14 , micro bio objects 15 , etc. ), terahertz systems 56 , 3D diffuse grayscale 57 and color 58 objects coding and imaging, computer-generated depth images representation 59 , next generation 3DTV applications 35,60 , quick volume scene displaying 61 , interferometry 15 , data multiplexing 62 , etc.…”

“…For off-axis 54 holograms, undesirable diffraction orders (zero-order and twin images) can be eliminated also 55 . Frequency filtering techniques are often used for reducing the informative holographic data size considerably 39,40 .…”