Accurate reconstruction in digital holographic microscopy using Fresnel dual-tree complex wavelet transform

The importance of Satellite Aperture Radar (SAR) imagery systems is increasing day-by-day in various field such as earth observation, hi-technology war mechanisms, etc. The images captured by SAR imagery systems are mainly used to detect and classify objects captured in the images. Due to the complexity of the image capturing process, SAR images can be highly noisy – often consisting of multiplicative noise, also known as speckle. To detect or classify objects in SAR images, speckle noise must be removed from images. During despeckling process, the preservation of important information in the SAR images while removing noise such as edge or patterns is a crucial task. Despeckling methods are liable to compromise on edge preservation ability while aspiring for good quality denoised images. Many researchers have proposed wavelet transform based despeckling approaches such as Discrete Wavelet Transform (DWT), Undecimated Wavelet Transform (UDWT), Dual Tree Complex Wavelet Transform (DTCWT). In these approaches, finding the best values of the coefficients plays an important role in yielding excellent denoised images with preserved edges. In this paper, we have proposed a novel optimization framework that optimizes thresholding coefficients of DTCWT despeckling method for SAR images. The proposed optimization framework is based on Fruit Fly Optimization (FOA) algorithm. The approach is a multi-objective optimization algorithm that is used to find maximum values for Peak Signal-to-Noise Ratio (PSNR), Mean Structural Similarity Index (MSSIM) and Equivalent number of look (ENL). The maximum value of MSSIM indicates high edge preservation capacity, whereas maximum PSNR value indicates good quality denoising of images. The maximum ENL value represents a good speckle-noise smoothing capability. We have applied our framework over some classical images as well as over SAR images of MSTAR dataset. In our experiments, we found that our proposed framework results in the excellent PSNR 36.87 dB, 35.4 dB and 37.8 dB, MSSIM values 0.92, 0.93 and 0.92, respectively, in the case of lena image, MSTAR dataset image and TerraSAR-X dataset image.

Motility, or co-ordinated movement, of cells is fundamental for the development of many processes, such as formation of the embryo, the immune response, inflammation, wound healing, and metastasis of cancer cells 1. Cells often migrate in response to specific external signals, but they can also move spontaneously. Aberrant cell motility can be fatal in cancer diseases when cells start to metastasize 2. Metastasis is strictly associated with tissue invasion of the primary tumor cells, and occurs as a multistep progress 3. The first phase of cancer cell metastasis involves the physical translocation of the cell to a distant organ, whereas the second phase implicates the ability of the cancer cell to develop into a metastatic lesion at that distant site 4. For skin cancer melanoma, the main cause of death is widespread metastases 5. Melanoma cells may travel along external vessel lattices. After settling in the metastatic sites, melanoma cells develop mechanisms that protect them against the attack of the immune system. It is, therefore, of great interest and importance to investigate, monitor, and understand the principles of tumor cell invasion and migration. The development of novel therapeutic applications that have the ability to block migratory processes is crucial. For in vitro studies, the cell culture wound-closure, and the transwell migration and invasion assays can provide data for an understanding how well a particular cell type can migrate 6. The wound healing assay is also called a scratch assay because it is performed by making a scratch in the cell monolayer (Fig. 1A). The transwell migration assay is a commonly used test to study the migratory response of endothelial cells to angiogenic inducers or inhibitors (Fig. 1B). This assay is also known as the Boyden or modified Boyden chamber assay. These assays have been frequently used to study movement of cells. Weckmann et al. developed an interesting system to monitor and quantify neutrophils on single cell level, by utilizing commercially available tissue culture hardware, simple video microscopic equipment, and standardized tracking 7. However, the interest for novel standardized real-time analyses using quantitative phase imaging (QPI) for cell tracking is growing (Fig. 2). More than 10 years ago, the digital holographic (DH) microscopy methodology of QPI became known to a larger audience and the technique has since then successfully been applied for label-free monitoring of live cells undergoing cell division, cell proliferation, cell death, and cell migration over time 8-10. By QPI, studies associated with both cellular thickness and refractive index fluctuations have been performed. The possibilities for utilizing QPI for cancer diagnostics have increased 11. Cellular behavior and phenotypes are other parameters that can be measured 12. For two human osteosarcoma cell types, the motility pattern, but not the proliferative pattern, was different. Early migration studies using DH microscopy showed fibroblast migration 13 and HT-1080 fibrosarcoma cells embedded in a 3D collagen gel 14. Alm et al. and Persson et al. also presented data on movement of different cell types and cell sizes 15 as well as demonstrated the correlation of cell movement with cell morphology 16. In the recent article published in the November 2018 issue of Cytometry Part A by Zhang et al., (pages 1125–1131) commercially available DH cytometry platforms equipped with semi-automated image acquisition, segmentation, and analysis software packages for assessing cell behavior are used and discussed. The motility data was obtained with QPI/cytometry using "Track cells module" and "Wound healing module," respectively, and with transwell migration assays determining migration and invasion, respectively. The different techniques assessing motility were compared. The two melanoma cell lines, WM793 and 1205Lu, used in the study were reported to have different metastatic capacity, resulting in differences in proliferation and motility. The motility measured with the "Track cells module" and "Wound healing module," using DH cytometry equipment housed in an incubator, produced highly correlated relative motilities, even when compared to the standard transwell migration and invasion assays. Images acquired with DH are from the same position in a cell culture vessel, making it possible to study individual cells. This is a strong advantage, since most studies of effects of new drugs on proliferation and migration of cancer cells in culture are performed on a population level. In a recent study by Kamlund et al., cell images were captured every fifth minute for a total of up to 72 h 17. For cell movement studies, the semi-automated algorithm attempts to find each tracked cell in the next frame by selecting the closest cell based on the centroid position. The advantages of the Track cells and Wound healing modules over the transwell migration and invasion assays in the paper by Zhang et al., included the possibility to use the cells in the experiment for other purposes after completing the measurement. DH microscopy also benefits from the fact that morphology analysis can be performed of each cell. Indeed, this opens up for almost unlimited possibilities to perform cell morphology analysis using the QPI methodology, since each image is very rich in cellular information. As discussed in a review by El-Schich et al., automated analysis and machine learning is one approach to handle the large amount of morphological data that can now be generated when analyzing cells with QPI 8. Only the computer resources and the training speed will set the limitations.

This paper focuses on the evaluation of noisy image fusion for medical images obtained from different modalities. In general, medical images suffer from poor contrast and are corrupted by blur and noise due to the imperfection of image capturing devices. In order to improve the visual and quantitative quality of the fused image, we compare two algorithms with other fusion techniques. The first algorithm is based on Dual Tree Complex Wavelet Transform (DTCWT) while the second is based on Scale Mixing Complex Wavelet Transform (SMCWT). The tested algorithms are using different fusion rules in each one, which leads to a perfect reconstruction of the output (fused image), this combination will create a new method which exploits the advantages of each method separately. DTCWT presents a good directionality since it considers the edge information in six directions and provide approximate shift invariant as well as SM-CWT, the goal of PCA is to extract the most significant features (wavelet coefficients in our case) to improve the spatial resolution. We compared the tested methods visually and quantitatively to recent fusion methods presented in the literature over several sets of medical images at multiple levels of noise. Further, the tested fusion algorithms have been tested up to the important level of Gaussian, salt & pepper and speckle noise (350 test). For the quantitative quality, we used several well-known fusion metrics. The results show that the tested methods outperform each method individually and other algorithms proposed in the literature.

Digital holographic microscopy (DHM) is an important technique that may be used for quantitative phase imaging of unstained biological cell samples. Since the DHM technology is not commonly used in clinics or bioscience research labs, at present there is no well-accepted focusing criterion for unstained samples that users can follow while recording image plane digital holograms of cells. The usual sharpness metrics that are useful for auto-focusing of stained cells do not work well for unstained cells as there is no amplitude contrast. In this work, we report a practical method for estimating the best focus plane for unstained cells in the digital hologram domain. The method is based on an interesting observation that for the best focus plane the fringe pattern associated with individual unstained cells predominantly shows phase modulation effect in the form of bending of fringes and minimal amplitude modulation. This criterion when applied to unstained red blood cells shows that the central dip in the doughnut-like phase profile of cells is maximal in this plane. The proposed methodology is helpful for standardizing the usage of DHM technology across different users and application developmentefforts. LAY DESCRIPTION: Digital holographic microscopy (DHM) is slowly but steadily becoming an important microscopy modality and gaining acceptability for basic bio-science research as well as clinical usage. One of the important features of DHM is that it allows users to perform quantitative imaging of unstained transparent cells. Instead of using dyes or fluorescent labelling, DHM systems use quantitative phase as a contrast mechanism which depends on the natural refractive index variation within the cell samples. Since minimal wet lab processing is required in order to image cell samples with a DHM, cells can be imaged in their natural state. While DHM is gaining popularity among users, the imaging protocols across the labs or users need to be standardized in order to make sure that the same quantitative phase parameters are used for tasks such as quantitative phased based cellclassification. One of the important operational tasks for any microscopy work is to focus the sample under study. While focusing comes naturally to users of brightfield microscopes based on image contrast, the focusing is not straightforward when samples are unstained so that they do not offer any amplitude contrast. When performing quantitative phase imaging, defocus can actually change the phase profile of the cell due to near-zone (Fresnel) diffraction effects. So unless a standardized focusing methodology is used, it will be difficult for multiple DHM users (potentially at different sites) to agree on quantitative results out of their phase images. DHM literature has prior works which perform numerical focusing of recovered complex wave-field in the hologram plane to find the best focus plane. However such methods are not user friendly and do not allow user the same focusing experience as in a brightfield microscope. The numerical focusing is therefore a reasonably good method for an optics researcher but not necessarily so for a microscopy technician looking at cell samples with a DHM system in a clinicalsetting. The present work provides a simple focusing criterion for unstained samples that works directly in the hologram domain. The technique is based on an interesting observation that the when an unstained cell sample is in the best-focus plane, its corresponding hologram (or fringe pattern) predominantly shows phase modulation manifested by bending of fringes at the location of the cell. This criterion can be converted into a simple numerical method as we have used to find the best-focus plane using a stack of through focus holograms. We believe that the technique can be used manually by visually observing the holograms or can be converted to an auto-focus algorithm for a motorized DHMsystem.

In this thesis, we describe new approaches and methods for reconstructing complex-valued wave fields from digital holograms. We focus on Fresnel holograms recorded in an off-axis geometry, for which operational real-time acquisition setups readily exist. The three main research directions presented are the following. First, we derive the necessary tools to port methods and concepts of wavelet-based approaches to the field of digital holography. This is motivated by the flexibility, the robustness, and the unifying view that such multiresolution procedures have brought to many applications in image processing. In particular, we put emphasis on space-frequency processing and sparse signal representations. Second, we propose to decouple the demodulation from the propagation problem, which are both inherent to digital Fresnel holography. To this end, we derive a method for retrieving the amplitude and phase of the object wave through a local analysis of the hologram's interference fringes. Third, since digital holography reconstruction algorithms involve a number of parametric models, we propose automatic adjustment methods of the corresponding parameters. We start by investigating the Fresnel transform, which plays a central role in both the modeling of the acquisition procedure and the reconstruction of complex wave fields. The study of the properties that are central to wavelet and multiresolution analysis leads us to derive Fresnelets, a new family of wavelet-like bases. Fresnelets permit the analysis of holograms with a good localization in space and frequency, in a way similar to wavelets for images. Since the relevant information in a Fresnel off-axis hologram may be separated both in space and frequency, we propose an approach for selectively retrieving the information in the Fresnelet domain. We show that in certain situations, this approach is superior to others that exclusively rely on the separation in space or frequency. We then derive a least-squares method for the estimation of the object wave's amplitude and phase. The approach, which is reminiscent of phase-shifting techniques, is sufficiently general to be applied in a wide variety of situations, including those dictated by the use of microscopy objectives. Since it is difficult to determine the reconstruction distance manually, we propose an automatic procedure. We take advantage of our separate treatment of the phase retrieval and propagation problems to come up with an algorithm that maximizes a sharpness metric related to the sparsity of the signal's expansion in distance-dependent Fresnelet bases. Based on a simulation study, we suggest a number of guidelines for deciding which algorithm to apply to a given problem. We compare existing and the newly proposed solutions in a wide variety of situations. Our final conclusion is that the proposed methods result in flexible algorithms that are competitive with preexisting ones and superior to them in many cases. Overall, they may be applied in a wide range of experimental situations at a low computational cost.

Process engineering and failure analysis of MEMS and MOEMS require static and dynamical characterization of both their in-plane and out of plane response to an excitation. A remarkable characteristic of Digital Holography Microscopes (DHM) is the extremely short acquisition time required to grab the whole information necessary to provide 3D optical topography of the sample: a unique frame grab, without any vertical or lateral scan provides the information over the full field of view. First, it ensures DHM measurements to be insensitive to vibrations. Second, it opens the door to fast dynamical characterization of micro-systems. For periodic movement analysis, DHM can operate in stroboscopic mode with standard cameras. It enables precise characterization up to excitation frequencies of 100 kHz with recovery cycle of 10% simply by triggering properly the camera. Pulsed sources can be used for investigation of higher excitation frequencies. For non periodic movement analysis fast acquisition cameras and postponed treatment are used. DHM are therefore unique and very efficient tool for dynamical characterization of in- plane and out-of-plane response. In this paper we show the basics of the technology and illustrate process engineering and failure analysis using DHM with an example of in and out of plane characterization of movements of a variable capacitor using the stroboscopic mode of acquisition.

Digital holography, as any other coherent imaging modalities, is subject to speckle noise. Speckles may degrade significantly the image quality, therefore many optical and digital techniques were developed to suppress the speckles. In this paper we present a comparison between six digital speckle filtering techniques used for digital holography.

In this work, we present a patented procedure that generates three dimensional (3D) image of a microscopic object with high definition, obtained by merging Scanning Electron Microscopy (SEM) and Digital Holography Microscopy (DHM) data. A high spatial resolution (up to r z =λ/20, r yx ≅100nm) 3D model of the object is generated starting from two digital images, acquired separately, following standard characterization procedures. Then, the two set of data are combined using an original mathematical algorithm, which has been implemented with a commercially available software. The developed methodology is of broad interest and has been applied to elements of biological interest, in order to prove its features.

In this paper, a novel filtering method is proposed for synthetic aperture radar (SAR) images by applying the dual-tree complex wavelet transform (DTCWT) with an adaptive quantum-inspired estimation of speckle noise variance. Firstly, an improved Laplacian probability distribution function (PDF) with an adaptive smoothing factor is built up for the complex wavelet coefficients of log-transformed image signal. And then, considering the inter-scale dependency and inner-scale relativity, the quantum-inspired probability of noise is introduced in the estimation of speckle noise variance. Finally, according to the Bayesian maximum a posteriori (MAP) theory, an adaptive despeckling method is proposed for SAR images. Experiments demonstrate effectiveness of the proposed method, which can notably reduce speckle noise and effectively preserve details of SAR image at the same time.KeywordsSpeckle noiseQuantum signal processing (QSP)Dual-tree complex wavelet transform (DTCWT)

The central goal of this dissertation is to design and model a smoothing filter based on the random single and mixed noise distribution that would attenuate the effect of noise while preserving edge details. Only then could robust, integrated and resilient edge detection methods be deployed to overcome the ubiquitous presence of random noise in images. Random noise effects are modeled as those that could emanate from impulse noise, Gaussian noise and speckle noise. In the first step, evaluation of methods is performed based on an exhaustive review on the different types of denoising methods which focus on impulse noise, Gaussian noise and their related denoising filters. These include spatial filters (linear, non-linear and a combination of them), transform domain filters, neural network-based filters, numerical-based filters, fuzzy based filters, morphological filters, statistical filters, and supervised learning-based filters. In the second step, switching adaptive median and fixed weighted mean filter (SAMFWMF) which is a combination of linear and non-linear filters, is introduced in order to detect and remove impulse noise. Then, a robust edge detection method is applied which relies on an integrated process including non-maximum suppression, maximum sequence, thresholding and morphological operations. The results are obtained on MRI and natural images. In the third step, a combination of transform domain-based filter which is a combination of dual tree – complex wavelet transform (DT-CWT) and total variation, is introduced in order to detect and remove Gaussian noise as well as mixed Gaussian and Speckle noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on medical ultrasound and natural images. In the fourth step, a smoothing filter, which is a feed-forward convolutional network (CNN) is introduced to assume a deep architecture, and supported through a specific learning algorithm, l2 loss function minimization, a regularization method, and batch normalization all integrated in order to detect and remove impulse noise as well as mixed impulse and Gaussian noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on natural images for both specific and non-specific noise-level.

This paper proposed a new OFDM system based on dual — tree complex wavelet transform (DTCWT). In this work, the advantages of the shift invariance property are shown from the results of the average bit error rate (BER) performance of the proposed system under different filters length. The results are compared with that of the conventional OFDM and wavelet packet modulation (WPM) in Rayleigh channel environment. Simulation results show the superior of the OFDM based on DTCWT over the conventional OFDM and WPM systems.

Super-resolved Mirau digital holography by structured illumination

In order to achieve high resolution quantitative imaging in digital holographic microscopy (DHM) typically microscope lenses with a high numerical aperture are applied. This results in a low depth of field (DOF) of the optical imaging system. Thus, for example, surfaces and specimens that cannot be imaged in parallel with the hologram recording device are recorded partly defocused. We explored the compensation of such defocusing effects by partial numerical propagation of the complex wave fields that are retrieved from digitally recorded off-axis holograms. The numerical propagation of small wave field parts with low pixel numbers is strongly affected by Fresnel diffraction and aliasing. Thus, the influence of these effects was quantified and used in an adapted algorithm for numerical refocusing of tilted image planes that considers the DOF of the applied optical imaging system. Results from simulations and experimental investigations show that typical numerical propagation artifacts origin from Fresnel diffraction which efficiently can be suppressed by an adequate adaptation of the numerical propagation. Data from the application of the resulting algorithm demonstrates that images planes with a tilt of up to 80 degrees to the hologram plane can be compensated.

Speckle noise reduction by multiple reconstructions in digital off axis holography

Speckle noise removal in SAR images using Multi-Objective PSO (MOPSO) algorithm