Determination of the point spread function of layered metamaterials assisted with the blind deconvolution algorithm

The main inherent property of medical ultrasound imaging is speckle noise which generally obscures and reduces the diagnostic image resolution and contrast. Consequently, the substantial improvement of ultrasound images is an important prerequisite, whenever ultrasound is used as one of the most utilized diagnostic modalities. The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as a prerequisite in ultrasound imaging processing in the recent decades. Recently, the Total Variation (TV) regularization method has become extremely effective approach for image reconstruction, especially for restoring edges of the blurring image. In this paper, we present a new blind iterative TV deconvolution algorithm for reconstructing ultrasound images from blurry and noisy observations. First, it proposes the initial estimation of the point-spread function (PSF) based on a generalization of two-dimensional homomorphic filtering in cepstrum domain. It is demonstrated that the initial PSF can be effectively estimated by applying a proper smoothing low-pass filtering in cepstrum domain. Second, it introduces a novel blind iterative TV deconvolution which is derived from an alternating minimization algorithm. Fast Fourier Transform (FFT) is used in the pre-iteration computation. The innovative blind deconvolution is based on either concurrent or successive estimation of the PSF function and the image of interest. The iterative scheme is devised to recover the image and simultaneously identify the PSF function. The estimated PSF and restored image will be close to real values in the subsequent iterative deconvolution. Final, tests on phantom and clinical images have proven our novel blind iterative TV deconvolution gives more positive results of higher spatial resolution and better defined tissue structures than other deconvolution methods.

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.

We propose a new method of blind deconvolution (BD) suitable for the recovery of truncated blurred images. In practical cases we often encounter truncated images, but they are difficult to treat properly with conventional BD algorithms, since nontruncated blurred images are assumed. The proposed method is based on simulated annealing (SA), to which we introduce an adaptive masking process. After a truncated segment is cut out from the blurred image, the sharp edges surrounding the segment are removed by multiplying the initial window, whose shape is determined with the initial estimate of the point spread function (PSF). A more appropriate estimate for the PSF is obtained from the masked segment based on the SA algorithm, and according to the new estimate of the PSF, the shape of the window is varied. These procedures are iterated until we finally obtain the best possible estimate of the PSF. In the last step, the entire blurred image is deconvolved with the final estimate of the PSF to obtain the recovered image. The effectiveness of the proposed method is confirmed by computer simulation.

There are a number of technical situations where inversion of measured data involves blind deconvolution (i.e. the point spread function is unknown a priori) in three (or more) dimensions. We show that a unique solution exists for three-dimensional (3D) blind deconvolution for a particular sampling of the Fourier transform of a blurred image whose average density is less than the Nyquist density. This suggests that 3D blind deconvolution problems may be easier to solve than 2D problems. Experiments using an iterative blind deconvolution algorithm indicate that convergence is faster for the 3D case than for the 2D case, and that reducing the sampling density has a rather small effect on the quality of reconstructions. >

The correction of an adaptive optics (AO) system is always partially, a post-processing technique such as blind deconvolution can be used to improve the image quality. In this paper, we propose a blind deconvolution algorithm using Zernike-polynomial-based phase fitting to recover a high resolution and contrast image from the short-exposure AO images. The strategy is to parameterize the point spread function (PSF) with phase aberrations pixel by pixel and introduce a constraint to the phase estimations using phase fitting. The algorithm is robust and can lead to a restoration free of artifacts. We evaluate the performance of our proposed algorithm by a number of simulated experiments and it is well performed.

EPID images are related to the fluence by a (possibly position‐dependent) Point Spread Function (PSF), or kernel. So far, work concerning finding the PSF for a certain EPID has relied on continuous representations. Since the EPID image itself corresponds to a discrete pixel grid, an interesting problem is to find a discrete PSF and do so based only on measurements, without resorting to Monte Carlo simulations. The present work concerns a method for finding such a discrete kernel for the simple case when the kernel is translation‐ and rotation‐invariant. The method relies on minimizing the difference, in a least‐squares sense, between the true acquired image and the image obtained with the calculated kernel. The method was tested using a simulated fluence and EPID image corresponding to a uniform rectangular field. The EPID image was generated by convolving the fluence with a known PSF. The developed algorithm was then tested by comparing the PSF shape produced by the algorithm (based on the image and fluence) with the actual PSF shape used to construct the EPID image. The two were found to match perfectly. A second test was performed by introducing a random error, uniformly distributed in the (−10%, +10%) interval, into the fluence used as input for the algorithm and then reconstructing the EPID image using the calculated PSF. The difference between the “true” EPID image and the reconstructed one was found to be smaller than 0.1% for the simulated field that was studied.

A computational camera uses a combination of optics and processing to produce images that cannot be captured with traditional cameras. Over the last decade, a range of computational cameras have been proposed, which use various optics designs to encode and use computation to decode useful visual information. What is often missing, however, is the quantitative analysis of the relation between camera design and the captured visual information, and little systematic work has been done to evaluate and optimize these computational camera designs. While the optics of computational cameras may be quite complicated, many of them can be effectively characterized by their point spread functions (PSFs): the intensity distribution on an image sensor as a response to a point light source in a scene. This thesis explores the techniques to characterize, evaluate and optimize computational cameras via PSF engineering for computer vision tasks, including image recovery, 3D reconstruction, and image refocusing. I first explore PSF engineering techniques to recover image details from blurry images. Image blur is a problem commonly seen in photography due to a number of reasons, including defocus, lens aberration, diffraction, atmospheric turbulence, object motion, and etc. Image blur is often formulated as a convolution of the latent blur-free image and a PSF, and deconvolution (or deblurring) techniques have to be used to recover image details from a blurry region. Here, I propose a comprehensive framework of PSF evaluation for the purpose of image deblurring, in which the effects of image noise, deblurring algorithm, and the structure of natural images are all taken into account. In defocus blur, the shape of defocus PSF is largely determined by the aperture pattern of the camera lens. By using an evaluation criterion derived from the comprehensive framework, I optimize the aperture pattern to preserve many more image details when defocus occurs. Both through simulations and experiments, I demonstrate the significant improvement gained by using optimized aperture patterns. While defocus blur causes a loss in image detail, it also encodes depth information of scenes in images. A typical depth from defocus (DFD) technique computes depth from two or more images that are captured with circular aperture lenses of different focus settings. Circular apertures produce circular defocus PSFs. In this thesis, I show that the use of a circular aperture severely restricts the accuracy of DFD, and propose a comprehensive framework of PSF evaluation for depth recovery. With this framework, we can derive a criterion for evaluating a pair of apertures with respect to the precision of depth recovery. This criterion is optimized using a genetic algorithm and gradient descent search to arrive at a pair of high resolution apertures. The two coded apertures are found to complement each other in the scene frequencies they preserve. With this property it becomes possible to not only recover depth with greater fidelity but also to obtain a high quality all-focused image from the two defocused images. While depth recovery can significantly benefit from optimized aperture patterns, its overall performance is rigidly limited by the lens aperture's physical size. To transcend this limitation, I propose a novel depth recovery technique using an optical diffuser - referred to as depth from diffusion (DFDiff). I show that DFDiff is analogous to conventional DFD, in which the scatter angle of the diffuser determines the system's effective aperture. High precision depth estimation can be achieved by choosing a proper diffuser and no longer requires the large lenses that DFD requires. Even a consumer camera with a low-end small lens can be used to do high-precision depth estimation when coupled with an optical diffuser. In my detailed analysis of the image formation properties of a DFDiff system, I show a number of examples demonstrating greater precision in depth estimation when using DFDiff. While the finite depth of field (DOF) of a lens camera leads to defocus blur, it also produces artistic visual experience. Many of today's displays are interactive in nature, which opens up a possibility for new kind of visual representations. Users could, for example, interactively refocus images to different depths, so that they can experience the artistic narrow DOF images while simultaneously making available the image detail for the entire image. To enable image refocusing, one typical approach is to capture the entire light field. But this method has the drawback of a significant sacrifice in spatial resolution due to the dimensionality gap: the captured information (light field) is 4D, while the required information (focal stack) is only 3D.In this thesis, I present an imaging system that directly captures focal stacks by a sweeping focal plane. First, I describe how to synchronize focus sweeping with image capturing so that the summed DOF of a focal stack efficiently covers the entire depth range. Then, I take a customized algorithm to enable a seamless refocusing experience, even in textureless regions or with moving objects. Prototype cameras are presented to capture real space-time focal stacks. There is also an interactive refocusing viewer available online at www.focalsweep.com.

An iterative blind deconvolution algorithm for degrade image is presented in this paper. The algorithm including two step, namely, the estimation of the point spread function of degrade image and the restoration using estimated point spread function. Two different Hopfield neural networks are built for realize the two steps. An iterative procedure is used to control the restoration process. The simulation results indicate that the method is effective for blind deconvolution with high convergence speed.

In order to alleviate the shortcomings of most blind deconvolution algorithms, this paper proposes an improved fast algorithm for blind deconvolution based on decorrelation technique and broadband block matrix. Althougth the original algorithm can overcome the shortcomings of current blind deconvolution algorithms, it has a constraint that the number of the source signals must be less than that of the channels. The improved algorithm deletes this constraint by using decorrelation technique. Besides, the improved algorithm raises the separation speed in terms of improving the computing methods of the output signal matrix. Simulation results demonstrate the validation and fast separation of the improved algorithm.

The present paper illustrates a geodesic-based learning algorithm over a curved parameter space for blind deconvolution application. The chosen deconvolving structure appears as a single neuron model whose learning rule arises from criterion-function minimization over a smooth manifold. In particular, we propose here a learning stepsize selection theory for the algorithm at hand. We consider the blind deconvolution performances of the algorithm as well as its computational burden. Also, a numerical comparison with seven blind-deconvolution algorithms known from the scientific literature is illustrated and discussed. Results of numerical tests conducted on a noiseless as well as a noisy system will confirm that the algorithm discussed in the present paper performs in a satisfactory way. Also, the performances of the presented algorithm will be compared with those exhibited by other blind deconvolution algorithms known from the literature.

Generally, blind super-resolution with unknown blurs is treated as an optimization problem. This involves a cost function, composed of terms accounting for changes in image and point spread function (PSF), which usually undergoes regularization due to the ill-posedness of the problem. In this paper, we introduce a novel regularization term for the PSF such that the spectral change in the image caused by degradation is also included. This is based on the fact that the presence of PSF in images affects the frequency component concentration. This cost function is optimized with respect to the image and the PSF in an alternating manner. Experiment results show that the proposed method is effective based on an objective evaluation method and that its PSF estimation accuracy is competitive in comparison with the recently proposed parametric method.

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.

A new blind deconvolution method with additional phase spectral constraints for the blurred image is discussed in this paper. The blurred image is a convolution of an original image and a point-spread function (PSF). The proposed method is based on the following iterative procedures, i.e., a projection onto a frequency space satisfying phase spectrum constraints, a minimization of a cost function and a projection onto an image space satisfying the support and nonnegativity constraints. This method restores the original image and the PSF stably with high accuracy. The effectiveness of the proposed method is verified by applying it to some blind deconvolution problems of images. The experimental results show that the performance of the proposed method is drastically improved in comparison with the conventional blind deconvolution method.

This study addresses the blind image deconvolution which uses only blurred image and less point spread function (PSF) information to restore the original image. To identify the blind image it is a very important step for restoring the image. Therefore, the first step is to look for PSF model. In this paper, particle swarm optimization (PSO) is utilized to seek the unknown PSF. The objective function is based on the wavelet transform. It can identify the parameters of PSF exactly. Finally, the feasibility and validity of proposed algorithm are demonstrated by several simulations.

We perform an analysis of the TRACE telescope blur from EUV images. Theblur pattern is discussed in terms of the telescope point-spread function (PSF) for the 171 A filter. The analysis performed consists of two steps. First, an initial shape for the PSF core is determined directly from TRACE EUV images. Second, the blind-deconvolution method is used for obtaining the final PSF shape. The PSF core peak is fitted by analytical functions to determine its parametric characteristics. The determined PSF includes the core central peak and peaks caused by diffraction effects inherent in TRACE EUV data. The diffraction portion of the PSF is studied theoretically in the Fraunhofer diffraction limit. The temperature dependence of the TRACE PSF shape is investigated for a selected temperature range. We also discuss general properties of the obtained PSF and its possible applications.