2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure

Spectral pre-modulation of training examples enhances the spatial resolution of the Phase Extraction Neural Network (PhENN)

The Phase Extraction Neural Network (PhENN) is a computational architecture, based on deep machine learning, for lens-less quantitative phase retrieval from raw intensity data. PhENN is a deep convolutional neural network trained through examples consisting of pairs of true phase objects and their corresponding intensity diffraction patterns; thereafter, given a test raw intensity pattern PhENN is capable of reconstructing the original phase object robustly, in many cases even for objects outside the database where the training examples were drawn from. Here, we show that the spatial frequency content of the training examples is an important factor limiting PhENN's spatial frequency response. For example, if the training database is relatively sparse in high spatial frequencies, as most natural scenes are, PhENN's ability to resolve fine spatial features in test patterns will be correspondingly limited. To combat this issue, we propose "flattening" the power spectral density of the training examples before presenting them to PhENN. For phase objects following the statistics of natural scenes, we demonstrate experimentally that the spectral pre-modulation method enhances the spatial resolution of PhENN by a factor of 2.Comment: 12 pages, 10 figure

NANOSCALE INVESTIGATION OF NUCLEAR STRUCTURES BY TIME-RESOLVED MICROSCOPY

The eukaryotic cell nucleus is composed by heterogeneous biological structures, such as the nuclear envelope (NE) and chromatin. At a morphological level, chromatin organization and its interactions with nuclear structures, such as nuclear lamina (NL) and nuclear pore complex (NPC), are suggested to play an essential role in the regulation of gene activity, which involves the packaging of the genome into transcriptionally active and inactive sites, bound to healthy cell proliferation and maintenance. However, the processes governing the relation between nuclear structures and gene regulation are still unclear. For this reason, the advanced microscopy methods represent a powerful tool for imaging nuclear structures at the nanometer level, which is essential to understand the effect of nuclear interactions on genome function. The nanometer information may be achieved either through the advanced imaging techniques in combination with fluorescence spectroscopy or with the help of super-resolution methods, increasing the spatial resolution of the conventional optical microscopy. In this thesis, I implemented a double strategy based on a novel FLIM-FRET assay and super resolution SPLIT-STED method for the investigation of the chromatin organization and nuclear envelope components (lamins and NPC) at the nanoscale, in combination with the phasor analysis. The phasor approach can be applied to several fluorescence microscopy techniques abled to provide an image with an additional information in a third channel. Phasor plot is a graphical representation, which decodes the fluorescence dynamics encoded in the image, revealing a powerful tool for the data analysis in time-resolved imaging. The Chapter 1 of the thesis is characterized by an Introduction, which provides an overview on the chromatin organization at the nanoscale and the description of the several advanced fluorescence microscopy techniques used for its investigation. They are broadly divided into two main categories: the advanced imaging techniques, such as Fluorescence Correlation Spectroscopy (FCS), single particle tracking (SPT) and Fluorescence Recovery After Photobleaching (FRAP), Forster Resonance Energy Transfer (FRET) and Fluorescence Lifetime Imaging Microscopy (FLIM) and the super-resolution techniques, which include Stimulated Emission Depletion (STED), Structured Illumination Microscopy (SIM) and single molecule localization microscopy (SMLM). Following, Chapter 2 focus on the capabilities of the phasor approach in time-resolved microscopy, as a powerful tool for the analysis of the experimental data. After a description of the principles of time-domain and frequency-domain measurements, in this section are explained the rules of the phasor analysis and its applications in different fluorescence microscopy techniques. In Chapter 3, I present a FRET assay, based on the staining of the nuclei with two DNA-binding dyes (e.g. Hoechst 33342 and Syto Green 13) by using frequency-domain detection of FLIM and the phasor analysis in live interphase nuclei. I show that the FRET level strongly depends on the relative concentration of the two fluorophores. I describe a method to correct the values of FRET efficiency and demonstrate that, with this correction, the FLIM-FRET assay can be used to quantify variations of nanoscale chromatin compaction in live cells. In Chapter 4, the phasor analysis is employed to the improvement of the resolving power of the super-resolution STED microscopy. I describe a novel method to investigate nuclear structures at the nanometer level, known as SPLIT (Separation of Photons by Lifetime Tuning), developed by my group in last years. By using the phasor approach, the SPLIT technique decodes the variations of spectroscopic parameters of fluorophores, such as lifetime and fluorescence intensity, due to the effect of the modulated depletion power of the STED technique, increasing the resolving power. In this chapter, I develop the concept of the SPLIT method modulating the excitation pattern during the image acquisition to overcome its limitation linked to the photobleaching effect and the signal-to-noise ratio

A concept for single-shot volumetric fluorescence imaging via orthogonally polarized excitation lattices.

The deconvolution of widefield fluorescence images provides only guesses of spatial frequency information along the optical axis due to the so called missing cone in the optical transfer function. Retaining the single-shot imaging speed of deconvolution microscopy while gaining access to missing cone information is thus highly desirable for microscopy of volumetric samples. Here, we present a concept that superimposes two orthogonally polarized excitation lattices with a phase-shift of p between them. In conjunction with a non-iterative image reconstruction algorithm this permits the restoration of missing cone information. We show how fluorescence anisotropy could be used as a method to encode and decode the patterns simultaneously and develop a rigorous theoretical framework for the method. Through in-silico experiments and imaging of fixed biological cells on a structured illumination microscope that emulates the proposed setup we validate the feasibility of the method

Successful optimization of reconstruction parameters in structured illumination microscopy

The impact of the different reconstruction parameters in super-resolution structured illumination microscopy (SIM) on image artifacts is carefully analyzed. These parameters comprise the Wiener filter parameter, an apodization function, zero-frequency suppression and modifications of the optical transfer function. A detailed investigation of the reconstructed image spectrum is concluded to be suitable for identifying artifacts. For this purpose, two samples, an artificial test slide and a more realistic biological system, were used to characterize the artifact classes and their correlation with the image spectra as well as the reconstruction parameters. In addition, a guideline for efficient parameter optimization is suggested and the implementation of the parameters in selected up-to-date processing packages (proprietary and open-source) is depicted. © 2018 The Author

Review of photoacoustic flow imaging: its current state and its promises

Flow imaging is an important method for quantification in many medical imaging modalities, with applications ranging from estimating wall shear rate to detecting angiogenesis. Modalities like ultrasound and optical coherence tomography both offer flow imaging capabilities, but suffer from low contrast to red blood cells and are sensitive to clutter artefacts. Photoacoustic imaging (PAI) is a relatively new field, with a recent interest in flow imaging. The recent enthusiasm for PA flow imaging is due to its intrinsic contrast to haemoglobin, which offers a new spin on existing methods of flow imaging, and some unique approaches in addition. This review article will delve into the research on photoacoustic flow imaging, explain the principles behind the many techniques and comment on their individual advantages and disadvantages

Investigation of a Tunable 3-D Patterned Illumination Design Implementation for Structured Illumination Microscopy

This thesis proposes methods to investigate a novel tunable incoherent 3D patterned illumination suitable for Structured Illumination Microscopy (SIM). A Matlab simulation was designed for the novel tunable illumination in a single and double slit configuration. An experimental setup of the single and double slit configurations was designed and used to acquire experimental data, which was compared with simulation predictions. The comparison aims to scrutinize the lateral and axial frequencies of the sinusoidal illiumination pattern and to determine the accuracy of the simulation with real world optics parameters. The simulation result provides a model of the the 3D patterned illumination, which is necessary for future use in a SIM setup. An accurate model of the illumination pattern will facilitate designing the forward and inverse SIM imaging models in a different study. The novel incoherent tunable illumination design will theoretically produce better super resolution and optical sectioning capability than current SIM setups that rely on coherent illumination