Modified K-factor image decomposition for three-dimensional super resolution microscopy

The three-dimensional (3D) imaging performance of a cone-beam computed tomography (CBCT) system can be quantitatively characterized by its 3D point spread function (PSF). To avoid the pitfalls associated with 3D PSF measurement through the use of a micro point phantom, we adopt an edge-based technique, which iteratively blurs a step edge into a spread edge with a Gaussian blurring kernel. In experiment, a small Teflon solid ball (diameter ~6mm) is used to provide step edges along the scanlines across the ball center, in terms of x-ray linear attenuation coefficient. Correspondingly, the spread edge profiles are extracted from the digital volume ball reconstructed by a CBCT system. From a spread edge profile, a step edge can be established by a rectification procedure (essentially an edge identification). A 1D PSF along a scanline is modeled as a Gaussian distribution, which is determined by iterative edge-blurring technique. The 1D PSFs on a cross section of the ball constitute a 2D PSF, and the 2D PSFs at three orthogonal cross sections are used to represent the 3D PSF at the position of the ball. By repositioning the ball phantom and repeating the procedure, we measured the 3D PSFs at 126 positions over half of the support space. Experiment shows that a CBCT system is of spatial variance and anisotropy in terms of FWHMs (full width at half maximum) of the blurring kernel. Both numerical and graphical presentations of PSF results are provided. As a result, the FWHM of the 3D PSF in our CBCT system varies in the range between 0.66 mm and 1.39 mm.

Cone-beam CT (CBCT) realizes true three-dimensional (3D) imaging in terms of its direct volume reconstruction with isotropic resolution. However, the 3D imaging performance of a CBCT system is spatially variant (or non-uniform) over the support domain, which can be quantitatively characterized by 3D point spread function (PSF). The CBCT system PSF can be experimentally measured through the use of telfon ball and edge-spread technique. For a single circular scan orbit, its volume reconstruction fails to meet data sufficiency condition, consequently causing spatial shift variance. In the pursuit of meeting data sufficiency condition, we have proposed a circle-plus-arc CB scan scheme. The overall CBCT imaging process involves several factors, including x-ray source, cone-beam projection, and computational reconstruction; each factor can in principle be characterized by a convolution kernel or PSF. In this paper, we concentrate on the PSF characterization of circle-plus-arc algorithm. Based on the linearity of Radon transform and inverse Radon transform, we can partition the Radon domain. In particular, the circle-plus-arc scan scheme partitions the Radon domain into a donut-like region (associated with the circle scan) and funnel-like null region (provided by the arc scan). A modified FDK algorithm is responsible for donut region reconstruction, and a filtered-backprojection-styled inverse Radon transform is for the null region reconstruction. By adding them up, we obtain the complete volume reconstruction. Through the use of a bead array phantom (a 5×5×5 array), subject to cone-beam scan under different scan patterns and volume reconstruction, we calculated the local PSF blurs and the spatial variance. The result shows that, for our CBCT simulation with 28 degree cone angle, the circle scan produces a spatial variance of 9.3% and the circle-plus-arc scan reduces that to 1.8%.

For cone-beam computed tomography (CBCT) systems, we propose a sphere phantom based method to estimate the full three-dimensional (3D) modulation transfer function (MTF). The FDK reconstruction of CBCT system in a local region was modeled by a triple convolution operator. Afterward, we calculated the directional projections of ideal and reconstructed sphere phantoms into a two-dimensional (2D) plane for multiple views. To estimate the projected 3D point spread function (PSF), we applied the 2D Richardson-Lucy deconvolution with Tikhonov-Miller (RL-TM). After estimating the projected 3D PSF from multiple views, the full 3D PSF was estimated by performing filtered backprojection. Then, the full 3D MTF was calculated by taking the modulus of the Fourier transform of the estimated 3D PSF. To validate the proposed method, we reconstructed sphere phantoms from simulation and experiment data. We simulated ideal 3D MTFs and compared them with the estimated 3D MTFs along the -, -, and -directions. The full-width at half-maximum (FWHM) and full-width at tenth-maximum (FWTM) values were compared between ideal and estimated 3D MTFs. The estimated 3D MTFs from both the simulation and experiment results show qualitative similarity in their shapes with the ideal 3D MTFs; FWHM and FWTM results quantitatively show that the proposed method provides reliable estimation performance. In particular, the estimated 3D MTF in a missing cone region was correctly matched with the corresponding ideal 3D MTF. In this work, we proposed a full 3D MTF estimation method for CBCT systems. Based on the results, we believe that the proposed method can be used to evaluate the spatial resolution performance of CBCT systems.

Three-dimensional images of confocal laser scanning microscopy suffer from a depth-variant blur, due to refractive index mismatch between the different mediums composing the system as well as the specimen, leading to optical aberrations. Our goal is to develop an image restoration method for 3D confocal microscopy taking into account the blur variation with depth. The difficulty is that optical aberrations depend on the refractive index of the biological specimen. The depth-variant blur function or the Point Spread Function (PSF) is thus different for each observation. A blind or semi-blind restoration method needs to be developed for this system. For that purpose, we use a previously developed algorithm for the joint estimation of the specimen function (original image) and the 3D PSF, the continuously depth-variant PSF is approximated by a convex combination of a set of space-invariant PSFs taken at different depths. We propose to add to that algorithm a pupil-phase constraint for the PSF estimation, given by the the optical instrument geometry. We thus define a blind estimation algorithm by minimizing a regularized criterion in which we integrate the Gerchberg-Saxton algorithm allowing to include these physical constraints. We show the efficiency of this method relying on some numerical tests.

We address the problem of computational representation of image formation in 3D widefield fluorescence microscopy with depth varying spherical aberrations. We first represent 3D depth-dependent point spread functions (PSFs) as a weighted sum of basis functions that are obtained by principal component analysis (PCA) of experimental data. This representation is then used to derive an approximating structure that compactly expresses the depth variant response as a sum of few depth invariant convolutions pre-multiplied by a set of 1D depth functions, where the convolving functions are the PCA-derived basis functions. The model offers an efficient and convenient trade-off between complexity and accuracy. For a given number of approximating PSFs, the proposed method results in a much better accuracy than the strata based approximation scheme that is currently used in the literature. In addition to yielding better accuracy, the proposed methods automatically eliminate the noise in the measured PSFs.

Adaptive optics (AO) enhances astronomical images by correcting perturbations in the optical system, resulting in complex point spread function (PSF) shapes, which provide critical information for optical design, calibration, and diagnostics. This paper presents a parametric model for an AO-corrected long-exposure PSF that adapts to complex shapes and various seeing conditions. A complementary estimation method is also introduced, addressing the inverse problem of estimating the atmospheric PSF or power spectral density (PSD) from observed PSF data. The model, based on Gaussian sum approximation (GSA), was tested using simulated PSF data from the OOMAO toolbox for Fried parameter (r0) values ranging from 0.10 to 0.20 m and on-sky data from the Very Large Telescope’s MUSE instrument. Two approaches were analyzed: (i) direct PSF estimation using GSA, and (ii) PSF estimation derived from atmospheric PSD estimation. Both methods were evaluated using root mean square error (RMSE). While approach (i) provided the best performance, approach (ii) produced more accurate atmospheric PSF estimates compared to the Moffat approximation and the Fetick method. Additionally, approach (ii) enabled the estimation of key physical parameters, such as the Fried parameter (r0) and residual AO variance ($\sigma _{AO}^2$). The proposed methods effectively estimate atmospheric PSF and PSD, even for complex PSF shapes influenced by spiders, central obstructions, or static aberrations.

Current amorphous silicon electronic portal imaging devices (a-Si EPIDs) that are frequently used in radiotherapy applications employ a metal plate/phosphor screen configuration to optimize x-ray detection efficiency. The phosphor acts to convert x rays into an optical signal that is detected by an underlying photodiode array. The dosimetric response of EPIDs has been well characterized, in part through the development of computational models. Such models, however, have generally made simplifying assumptions with regards to the transport of optical photons within these detectors. The goal of this work was to develop and experimentally validate a new Monte Carlo (MC) model of an a-Si EPID that simulates both x-ray and optical photon transport in a self-contained manner. Using this model the authors establish a definitive characterization of the effects of optical transport on the dosimetric response of a-Si EPIDs employing gadolinium oxysulfide phosphor screens. The Geant4 MC toolkit was used to develop a model of an a-Si EPID that employs standard electromagnetic and optical physics classes. The sensitivity of EPID response to uncertainties in optical transport parameters was evaluated by investigating their effects on the EPID point spread function (PSF). An optical blur kernel was also calculated to isolate the component of the PSF resulting purely from optical transport. A 6 MV photon source model was developed and integrated into the MC model to investigate EPID dosimetric response. Field size output factors and relative dose profiles were calculated for a set of open fields by separately scoring energy deposited in the phosphor and optical absorption events in the photodiode. These were then compared to quantify effects resulting from optical photon transport. The EPID model was validated against experimental measurements taken using a research EPID. Optical photon scatter within the phosphor screen noticeably broadened the PSF. Variations in optical transport parameters reported in the literature caused fluctuations in the PSF full width at half maximum (FWHM) and full width at tenth maximum (FWTM) of less than 3% and 5%, respectively, confirming model robustness. Greater deviations (up to 9.5% and 36% for FWHM and FWTM, respectively) were observed when optical parameters were largely different from reference values. When scoring energy deposition in the phosphor, measured and calculated output factors agreed within statistical uncertainties and at least 94% of the MC simulated profile data points passed 3%/3 mm γ-index criterion for all field sizes considered. Despite statistical uncertainties in optical simulations arising from computational limitations, no differences were observed between optical and energy deposition profiles. Simulations demonstrated noticeable blurring of the EPID PSF when scoring optical absorption events in the photodiode relative to energy deposition in the phosphor. However, modeling the standard electromagnetic transport alone should suffice when using MC methods to predict EPID dose-response to static, open 6 MV fields with a standard a-Si photodiode array. Therefore, using energy deposition in the phosphor as a surrogate for EPID dose-response is a valid approach that should not require additional corrections for optical transport effects in current a-Si EPIDs employing phosphor screens.

Localization microscopy relies on computationally efficient Gaussian approximations of the point spread function for the calculation of fluorophore positions. Theoretical predictions show that under specific experimental conditions, localization accuracy is significantly improved when the localization is performed using a more realistic model. Here, we show how this can be achieved by considering three-dimensional (3-D) point spread function models for the wide field microscope. We introduce a least-squares point spread function fitting framework that utilizes the Gibson and Lanni model and propose a computationally efficient way for evaluating its derivative functions. We demonstrate the usefulness of the proposed approach with algorithms for particle localization and defocus estimation, both implemented as plugins for ImageJ.

The presented work is concerned with the morphological description of stars and galaxies in the framework of the shapelet method. This method constitutes a linear expansion in the orthonormal set of Gauss-Hermite polynomials. Its main advantages – linearity, compactness, invariance under Fourier transformation, and the relation to the moments of the brightness distribution – are extensively discussed. The practical treatment of the image decomposition and of the deconvolution from the point spread function are further elaborated. Moreover, three fields of application are presented together with new investigations on the applicability and validity of the method: weak gravitational lensing, morphological class discovery, and realistic simulation of extragalactic observations.

Diffraction imaging spectrometer cannot acquire imaging spectral data without calculation and inversion. In this paper, the imaging process of the diffraction imaging spectrometer and the principle of the data error from both space and spectra are analyzed. To solve the problems of low definition of the reconstruction and the ringing in it occurring under the condition that the point spread function (PSF) is larger, a new algorithm is proposed based on improved inverse Wiener filtering. The improved method regards the reconstruction result of Wiener filtering as a new fuzzy image, and recalculates the PSF of the new fuzzy image based on the analysis of the diffraction characteristics and error. Inverse iterative Wiener filtering is used to improve the definition of the reconstruction, and then the noise needs to be removed according to the distribution of the spatial and spectral features. Simulated diffraction imaging spectral data are used to verify the correctness of the algorithm proposed in this paper. A reconstruction without ringing can be obtained when the standard deviation of PSF is 2.5, and both of the definition and detail ability are higher than those of the traditional reconstruction. The reconstruction using the improved algorithm proposed in this paper can satisfy the applications of the diffraction imaging spectral data.

Circular Synthetic Aperture Sonar (CSAS) processing computes coherently Synthetic Aperture Sonar (SAS) data acquired along a circular trajectory. This approach has a number of advantages, in particular it maximises the aperture length of a SAS system, producing very high resolution sonar images. CSAS image reconstruction using back-projection algorithms, however, introduces a dissymmetry in the impulse response, as the imaged point moves away from the centre of the acquisition circle. This paper proposes a sampling scheme for the CSAS image reconstruction which allows every point, within the full field of view of the system, to be considered as the centre of a virtual CSAS acquisition scheme. As a direct consequence of using the proposed resampling scheme, the point spread function (PSF) is uniform for the full CSAS image. Closed form solutions for the CSAS PSF are derived analytically, both in the image and the Fourier domain. The thorough knowledge of the PSF leads naturally to the proposed adapted atom waves basis for CSAS image decomposition. The atom wave deconvolution is successfully applied to simulated data, increasing the image resolution by reducing the PSF energy leakage.

We present a study comparing the accuracy of superlocalization imaging of plasmon-mediated emission from gold nanorods (AuNRs) using both Gaussian and dipole emission point-spread function (PSF) models. By fitting the emission PSF of single AuNR luminescence, we have shown that a 3-axis dipole PSF gives improved localization accuracy over the Gaussian PSF, especially for nonplanar AuNRs, while also allowing the AuNR three-dimensional orientation and emission wavelength to be determined. On the other hand, when a single-axis dipole PSF model is applied to the AuNR emission, the fit estimates converge to values that are inconsistent with their experimentally measured values, affecting both the localization accuracy and precision of the fitted centroid position. These results indicate that when applying superlocalization techniques to plasmonic nanostructures, care must be taken to understand the nature of the emission before a correct dipole PSF can be applied.

Super-resolution microscopy with phase masks is a promising technique for 3D imaging and tracking. Due to the complexity of the resultant point spread functions, generalized recovery algorithms are still missing. We introduce a 3D super-resolution recovery algorithm that works for a variety of phase masks generating 3D point spread functions. A fast deconvolution process generates initial guesses, which are further refined by least squares fitting. Overfitting is suppressed using a machine learning determined threshold. Preliminary results on experimental data show that our algorithm can be used to super-localize 3D adsorption events within a porous polymer film and is useful for evaluating potential phase masks. Finally, we demonstrate that parallel computation on graphics processing units can reduce the processing time required for 3D recovery. Simulations reveal that, through desktop parallelization, the ultimate limit of real-time processing is possible. Our program is the first open source recovery program for generalized 3D recovery using rotating point spread functions.

This work concentrates on the analysis of radar signature signals for the characterization and efficient computational of finite discrete 2D point spread functions. A general simple model for ground penetrating raw data image formation is assumed in order to concentrate on the efficient computation of point spread functions. The point spread functions are used as impulse response functions for the simulation of high resolution image of 2D synthetic aperture imaging kernels. A methodology has been developed to serve as a tool aid in the analysis, design, and efficient implementation of 1D and 2D fast Fourier transform (FFT) algorithms prevalent in SAR image formation operations with the idea in mind of reducing the computational effort and improving the hardware implementation process. Kronecker products algebra, a branch of finite dimensional multilinear algebra, has been demonstrated to be a useful tool aid in the development of fast algorithms for unitary transformations and in the identification of similarities and differences among FFT computational frameworks.

Historically, metallicity profiles of galaxies have been modelled using a radially symmetric, two-parameter linear model, which reveals that most galaxies are more metal-rich in their central regions than their outskirts. However, this model is known to yield inaccurate results when the point spread function (PSF) of a telescope is large. Furthermore, a radially symmetric model cannot capture asymmetric structures within a galaxy. In this work, we present an extension of the popular forward-modelling Python package lenstronomy, which allows the user to overcome both of these obstacles. We demonstrate the new features of this code base through two illustrative examples on simulated data. First, we show that through forward modelling, lenstronomy is able to recover accurately the metallicity gradients of galaxies, even when the PSF is comparable with the size of a galaxy, as long as the data are observed with a sufficient number of pixels. Additionally, we demonstrate how lenstronomy is able to fit irregular metallicity profiles to galaxies that are not well-described by a simple surface brightness profile. This opens up pathways for detailed investigations into the connections between morphology and chemical structure for galaxies at cosmological distances using the transformative capabilities of JWST. Our code is publicly available and open source, and can also be used to model spatial distributions of other galaxy properties that are traced by its surface brightness profile.