Sparsity-based multi-height phase recovery in holographic microscopy

Abstract

High-resolution imaging of densely connected samples such as pathology slides using digital in-line holographic microscopy requires the acquisition of several holograms, e.g., at >6–8 different sample-to-sensor distances, to achieve robust phase recovery and coherent imaging of specimen. Reducing the number of these holographic measurements would normally result in reconstruction artifacts and loss of image quality, which would be detrimental especially for biomedical and diagnostics-related applications. Inspired by the fact that most natural images are sparse in some domain, here we introduce a sparsity-based phase reconstruction technique implemented in wavelet domain to achieve at least 2-fold reduction in the number of holographic measurements for coherent imaging of densely connected samples with minimal impact on the reconstructed image quality, quantified using a structural similarity index. We demonstrated the success of this approach by imaging Papanicolaou smears and breast cancer tissue slides over a large field-of-view of ~20 mm2 using 2 in-line holograms that are acquired at different sample-to-sensor distances and processed using sparsity-based multi-height phase recovery. This new phase recovery approach that makes use of sparsity can also be extended to other coherent imaging schemes, involving e.g., multiple illumination angles or wavelengths to increase the throughput and speed of coherent imaging.

Reconstruction of in-line holograms: combining model-based and regularized inversion

“…The choices of the Mie model and the Rayleigh-Sommerfeld propagation make the proposed method adapted to a large domain of validity extending to absorbing and/or dephasing spherical objects and transmittance planes without any restriction on the recording distance. Thus, other applications can be considered such as lens-free microscopy [4,5,7,34] or in-line microscopy in biology [11,14,24] where the Lorenz-Mie model fitting and the non-parametric reconstruction techniques have independently shown their efficiency. The proposed method would be particularly well suited to reconstruct samples in which spherical objects are present among objects of more complex shapes [35,36].…”

“…These interferences are sensitive to the amplitude changes and phase shifts induced by the objects, making this technique particularly suitable for image and study absorbing and/or phase samples. Today, this high sensitivity is used in numerous fields including biology [2][3][4][5][6][7], fluid mechanics [8][9][10][11], and particle characterization [12][13][14].…”

“…The addition of physical constraints and wisely chosen regularizations is then necessary to solve the illposed problem, in so-called "non-parametric" approaches. Recent works have demonstrated the feasibility of such regularized reconstructions to retrieve the lost phase information from a single in-line hologram of absorbing and/or phase objects [4,23,24]. Penalized-likelihood image reconstruction [25], Maximum A Posteriori [26] and Compressive sensing [27][28][29] frameworks belong to this second class of methods.…”

From Fienup’s phase retrieval techniques to regularized inversion for in-line holography: tutorial

“…Most phase retrieval techniques are still derived from the methods of alternating projections initially proposed by Gerchberg and Saxton [3] and popularized and extended by Fienup [4,5]. This class of methods is still widely used today [6][7][8][9][10][11][12][13], with improvements to enforce a priori knowledge (support of the objects, admissible values domain, sparsity constraints) [14][15][16].…”

Subsampled phase retrieval for temporal resolution enhancement in lensless on-chip holographic video

“…As with the compressive video recovery schemes above, phase retrieval must also assume some prior knowledge about the imaged sample to ensure accurate algorithm convergence. Examples include a known finite sample support [18,19], sparsity [20], non-negativity or an intensity histogram [21]. Several recent works examine how sample sparsity permits accurate sample reconstruction from a limited number of holographic measurements [15,[22][23][24][25][26][27][28][29][30].…”