Studies on the sparsifying operator in compressive digital holography

ADMM-inspired image reconstruction for terahertz off-axis digital holography

Image reconstruction in off-axis terahertz digital holography is complicated due to the harsh recording conditions and the non-convexity form of the problem. In this paper, we propose an inverse problem-based reconstruction technique that jointly reconstructs the object field and the amplitude of the reference field. Regularization in the wavelet domain promotes a sparse object solution. A single objective function combining the data-fidelity and regularization terms is optimized with a dedicated algorithm based on an alternating direction method of multipliers framework. Each iteration alternates between two consecutive optimizations using projections operating on each solution and one soft thresholding operator applying to the object solution. The method is preceded by a windowing process to alleviate artifacts due to the mismatch between camera frame truncation and periodic boundary conditions assumed to implement convolution operators. Experiments demonstrate the effectiveness of the proposed method, in particular, improvements of reconstruction quality, compared to two other methods.

Advances in Digital Holographic Interferometry

Holographic interferometry is a well-established field of science and optical engineering. It has a half-century history of successful implementation as the solution to numerous technical tasks and problems. However, fast progress in digital and computer holography has promoted it to a new level of possibilities and has opened brand new fields of its application. In this review paper, we consider some such new techniques and applications.

Influence of sparse constraint functions on compressive holographic tomography

In this paper, we quantified and analyzed the impact of the l₁ norm and total variation (TV) norm sparse constraints on the reconstruction quality under different interlayer spacings, sampling rates, and signal-to-noise ratios. For high-quality holograms, the results of compressive-sensing reconstruction using l₁ norm achieved higher quality than those by the TV norm. In contrast, for low-quality holograms, the quality of TV-norm-based reconstruction results was relatively stable and better than that of l₁ norm. In addition, we explained why interlayer spacing cannot be smaller and recommend the use of axial resolution of the digital holography system as the interlayer spacing. The conclusions are valuable in the choice of sparse constraints in compressive holographic tomography.

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

In previous work [Opt. Lett.44, 2827 (2019)OPLEDP0146-959210.1364/OL.44.002827], we presented a method based on digital holography and orthogonal matching pursuit, which is able to determine the 3D positions of small objects moving within a larger motionless object. Indeed, if the scattering density is sparse in direct 3D space, compressive sensing algorithms can be used. The method was validated by imaging red blood cell trajectories in the trunk vascular system of a zebrafish (Danio rerio) larva. We give here further details on the reconstruction technique and present a more robust version of the algorithm based on multiple illuminations.

Wave atoms for digital hologram compression

Compression of macroscopic digital holograms is a major research problem, which if unresolved will continue to limit the possible applications of holography in multimedia contexts. The quest of searching for the most suitable representation for compression is still an open problem. In this work, we study sparsification by the wave atom transform, introduced in 2006 by Demanet et al., and experiment on four large-scale representative diffuse macroscopic holograms while testing compressibility in the object plane, Fourier plane, and defocused plane representations, respectively. We demonstrate that it is a suitable nonadaptive, sparsifying transform for Fourier or defocused content, and by integration into the wave atom coding (WAC) method, we sketch a full-fledged codec for the compression of macroscopic holograms. WAC is compared to two variants of JPEG 2000, with equal complexity of coding tools, and the more recent High Efficiency Video Coding (H.265/HEVC). For Fourier and defocused holograms, WAC outperforms the JPEG 2000 variants by 0.9-7.9 dB Bjøntegaard-Delta peak signal to noise ratio, especially in the former case, while it is as good as or better than even H.265/HEVC for very deep computer-generated holograms, thus improving on existing approaches.

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

Compression of digital holograms allows one to store, transmit, and reconstruct large sets of holographic data. There are many digital image compression methods, and usually wavelets are used for this task. However, many significant specialties exist for compression of digital holograms. As a result, it is preferential to use a set of methods that includes filtering, scalar and vector quantization, wavelet processing, etc. These methods in conjunction allow one to achieve an acceptable quality of reconstructed images and significant compression ratios. In this paper, wavelet compression of amplitude/phase and real/imaginary parts of the Fourier spectrum of filtered off-axis digital holograms is compared. The combination of frequency filtering, compression of the obtained spectral components, and extra compression of the wavelet decomposition coefficients by threshold processing and quantization is analyzed. Computer-generated and experimentally recorded digital holograms are compressed. The quality of the obtained reconstructed images is estimated. The results demonstrate the possibility of compression ratios of 380 using real/imaginary parts. Amplitude/phase compression allows ratios that are a factor of 2-4 lower for obtaining similar quality of reconstructed objects.

Optimized sensing of sparse and small targets using lens-free holographic microscopy

Lens-free holographic microscopy offers sub-micron resolution over an ultra-large field-of-view >20 mm², making it suitable for bio-sensing applications that require the detection of small targets at low concentrations. Various pixel super-resolution techniques have been shown to enhance resolution and boost signal-to-noise ratio (SNR) by combining multiple partially-redundant low-resolution frames. However, it has been unclear which technique performs best for small-target sensing. Here, we quantitatively compare SNR and resolution in experiments using no regularization, cardinal-neighbor regularization, and a novel implementation of sparsity-promoting regularization that uses analytically-calculated gradients from Bayer-pattern image sensors. We find that sparsity-promoting regularization enhances the SNR by ~8 dB compared to the other methods when imaging micron-scale beads with surface coverages up to ~4%.

Regularized reconstruction of absorbing and phase objects from a single in-line hologram, application to fluid mechanics and micro-biology

Reconstruction of phase objects is a central problem in digital holography, whose various applications include microscopy, biomedical imaging, and fluid mechanics. Starting from a single in-line hologram, there is no direct way to recover the phase of the diffracted wave in the hologram plane. The reconstruction of absorbing and phase objects therefore requires the inversion of the non-linear hologram formation model. We propose a regularized reconstruction method that includes several physically-grounded constraints such as bounds on transmittance values, maximum/minimum phase, spatial smoothness or the absence of any object in parts of the field of view. To solve the non-convex and non-smooth optimization problem induced by our modeling, a variable splitting strategy is applied and the closed-form solution of the sub-problem (the so-called proximal operator) is derived. The resulting algorithm is efficient and is shown to lead to quantitative phase estimation on reconstructions of accurate simulations of in-line holograms based on the Mie theory. As our approach is adaptable to several in-line digital holography configurations, we present and discuss the promising results of reconstructions from experimental in-line holograms obtained in two different applications: the tracking of an evaporating droplet (size ∼ 100μm) and the microscopic imaging of bacteria (size ∼ 1μm).

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

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.