Optical microscopy is an essential tool in biology and medicine. Imaging thin, yet non-flat objects in a single shot (without relying on more sophisticated sectioning setups) remains challenging as the shallow depth of field that comes with highresolution microscopes leads to unsharp image regions and makes depth localization and quantitative image interpretation difficult. Here, we present a method that improves the resolution of light microscopy images of such objects by locally estimating image distortion while jointly estimating object distance to the focal plane. Specifically, we estimate the parameters of a spatiallyvariant Point Spread Function (PSF) model using a Convolutional Neural Network (CNN), which does not require instrument- or object-specific calibration. Our method recovers PSF parameters from the image itself with up to a squared Pearson correlation coefficient of 0.99 in ideal conditions, while remaining robust to object rotation, illumination variations, or photon noise. When the recovered PSFs are used with a spatially-variant and regularized Richardson-Lucy (RL) deconvolution algorithm, we observed up to 2.1 dB better Signal-to-Noise Ratio (SNR) compared to other Blind Deconvolution (BD) techniques. Following microscope-specific calibration, we further demonstrate that the recovered PSF model parameters permit estimating surface depth with a precision of 2 micrometers and over an extended range when using engineered PSFs. Our method opens up multiple possibilities for enhancing images of non-flat objects with minimal need for a priori knowledge about the optical setup.

We present a semi-blind, spatially-variant deconvolution technique aimed at optical microscopy that combines a local estimation step of the point spread function (PSF) and deconvolution using a spatially variant, regularized Richardson-Lucy algorithm [1]. To find the local PSF map in a computationally tractable way, we train a convolutional neural network to perform regression of an optical parametric model on synthetically blurred image patches. We deconvolved both synthetic and experimentally-acquired data, and achieved an improvement of image SNR of 1.00 dB on average, compared to other deconvolution algorithms.

Deconvolution offers an effective way to improve the resolution of optical microscopy data. While fast algorithms are available when the point spread function (PSF) is shift-invariant (SI), they are not directly applicable in thick samples, where the problem is shift-variant (SV). Here, we propose a fast iterative shrinkage/thresholding 3D deconvolution method that uses different PSFs at every depth. This is realized by modeling the imaging system as a multi-rate filter-bank, with each channel corresponding to a distinct 3D PSF dependent on the position along the optical axis. The complexity associated with the thresholded Landweber update in each iteration of our SV algorithm is equivalent to that of an iteration in an SI algorithm, multiplied by the number of channels in the filter-bank. We simulated images of a set of beads embedded in an aqueous gel, using varying PSFs along the optical axis, to illustrate the effectiveness of our algorithm.

Current methods to build dynamic optical coherence tomography (OCT) volumes of the beating embryonic heart involve synchronization of 2D+time slice-sequences acquired over separate heartbeats. Temporal registration of these sequences is performed either through gating or postprocessing. While synchronization algorithms that exclusively rely on image- intrinsic signals allow forgoing external gating hardware, they are prone to error accumulation, require operator-supervised correction, or lead to nonisotropic resolution. Here, we propose an image-based, retrospective reconstruction technique that uses two sets of parallel 2D+T slice-sequences, acquired perpendicularly to each other, to yield accurate and automatic reconstructions with isotropic resolution. The method utilizes the similarity of the data at the slice intersections to spatio-temporally register the two sets of slice sequences and fuse them into a high-resolution 4D volume. We characterize our method by using 1) simulated heart phantom datasets and 2) OCT datasets acquired from the beating heart of live cultured E9.5 mouse and E10.5 rat embryos. We demonstrate that while our method requires greater acquisition and reconstruction time compared to methods that use slices from a single direction, it produces more accurate and self-validating reconstructions since each set of reconstructed slices acts as a reference for the slices in the perpendicular set.

Capturing the dynamics of individual structures in the embryonic heart is an essential step for studying its function and development. Label-free brightfield (BF) microscopy allows for higher acquisition frame-rates than techniques requiring molecular labeling, without interfering with embryo viability or needing complex equipment. However, since different structures contribute similarly to image contrast, label-free microscopy lacks specificity. Here we mitigate this problem by separating a single-channel image series into multiple channels specific to different cardio-vascular structures, based only on their motion patterns. The technique combines images from multiple cardiac cycles and z-sections after non-uniform temporal registration to produce 3D+time image volumes of one full cardiac cycle with separate channels for static, transient and periodically moving structures. The resulting data is well-suited for velocity analysis and 3D-visualization. We characterize the separating capabilities of our technique on a synthetic cardiac dataset and demonstrate its practical applicability, by reconstructing three-channel views of the beating embryonic zebrafish heart with an effective frame rate of 1000 volumes (256×256×20 voxels each) per second. This technique enables quantitative characterization of dynamic heart function during cardiogenesis.

We propose a construction of new wavelet-like bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCD-arrays. The starting point is a wavelet basis of L2 to which we apply a unitary Fresnel transform. The transformed basis functions are shift-invariant on a level-by-level basis but their multiresolution properties are governed by the special form that the dilation operator takes in the Fresnel domain. We derive a Heisenberg-like uncertainty relation that relates the localization of Fresnelets with that of their associated wavelet basis. According to this criterion, the optimal functions for digital hologram processing turn out to be Gabor functions, bringing together two separate aspects of the holography inventor's work. We give the explicit expression of orthogonal and semi-orthogonal Fresnelet bases corresponding to polynomial spline wavelets. This special choice of Fresnelets is motivated by their near-optimal localization properties and their approximation characteristics. We then present an efficient multiresolution Fresnel transform algorithm, the Fresnelet transform. This algorithm allows for the reconstruction (backpropagation) of complex scalar waves at several user-defined, wavelength-independent resolutions. Furthermore, when reconstructing numerical holograms, the subband decomposition of the Fresnelet transform naturally separates the image to reconstruct from the unwanted zero-order and twin image terms. This greatly facilitates their suppression. We show results of experiments carried out on both synthetic (simulated) data sets as well as on digitally acquired holograms.

We present an explicit formula for B-spline convolution kernels; these are defined as the convolution of several B-splines of variable widths h(i) and degrees n(i). We apply our results to derive spline-convolution-based algorithms for two closely related problems: the computation of the Radon transform and of its inverse. First, we present an efficient discrete implementation of the Radon transform that is optimal in the least-squares sense. We then consider the reverse problem and introduce a new spline-convolution version of the filtered back-projection algorithm for tomographic reconstruction. In both cases, our explicit kernel formula allows for the use of high-degree splines; these offer better approximation performance than the conventional lower-degree formulations (e.g., piecewise constant or piecewise linear models). We present multiple experiments to validate our approach and to find the parameters that give the best tradeoff between image quality and computational complexity. In particular, we find that it can be computationally more efficient to increase the approximation degree than to increase the sampling rate.