Studies on the sparsifying operator in compressive digital holography

Abstract

In compressive digital holography, we reconstruct sparse object wavefields from undersampled holograms by solving an ℓ-minimization problem. Applying wavelet transformations to the object wavefields produces the necessary sparse representations, but prior work clings to transformations with too few vanishing moments. We put several wavelet transformations belonging to different wavelet families to the test by evaluating their sparsifying properties, the number of hologram samples that are required to reconstruct the sparse wavefields perfectly, and the robustness of the reconstructions to additive noise and sparsity defects. In particular, we recommend the CDF 9/7 and 17/11 wavelet transformations, as well as their reverse counter-parts, because they yield sufficiently sparse representations for most accustomed wavefields in combination with robust reconstructions. These and other recommendations are procured from simulations and are validated using biased, noisy holograms.

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

“…Many popular methods of compression based on quantization, wavelets, and standard techniques of image compression are given in 12 , but comparisons and assessments of reconstruction quality are not given. 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 .…”

“…In summary, in the majority of these papers, contrastive analyses of techniques of extra compression of wavelet coefficients (for example, various means of quantization) were not performed.Complex-valued holographic images (i.e., used in phase-shifting holography 52 ) are usually given in articles focused on compression 12,17 . The corresponding object wave is often compressed (after preliminarily recording a number of phase-shifted digital holograms and filtering of twin and zero-order images) 20,22,51 . 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 .…”

“…Complex-valued holographic images (i.e., used in phase-shifting holography 52 ) are usually given in articles focused on compression 12,17 . The corresponding object wave is often compressed (after preliminarily recording a number of phase-shifted digital holograms and filtering of twin and zero-order images) 20,22,51 . Only a few papers have addressed single digital hologram compression and only compression of the amplitude matrix has been considered 53 .…”

4D compressive sensing holographic imaging of small moving objects with multiple illuminations

“…x, y, z), their 3D scattering density is sparse, which allows to apply compressive sensing reconstruction methods. In this specific case, the use of sparsifying operators [28] is not required. We used an algorithm based on orthogonal matching pursuit (OMP).…”

Coefficients Quantization at Off-axis Digital Hologram Wavelet Compression

“…However results of reconstruction quality comparison were not given. In the paper [23] cases of application of several wavelets in compressive digital holography are considered in detail, but there is no assessment of methods of direct truncating of wavelet coefficients.…”