Blind deconvolution subject to sparse representation for fluorescence microscopy

The objective of the paper was to validate non-linear parametric models of computerised tomography point spread function (PSF), to investigate the role of model parameters and to verify the effect of different imaging conditions on estimated parameters. These models were then to be used experimentally to estimate the variation of PSF shape within the field of view of a scanner. Two parametric models of the PSF are presented. The Gaussian model is appropriate when PSF values are positive, and the damped cosine model can account for negative values. These models are non-linear and fully two-dimensional and do not assume radial symmetry. The models were fitted to images of a point source. The models accounted for over 99% of the variance in the PSF signal. Errors in modulation transfer function were limited to 5% when the appropriate model was selected. The difference in the blurring characteristics of three image reconstruction filters was well quantified by shape parameters, and position parameters located the PSF with subpixel accuracy. With a point source located 50mm directly above the centre of the field of view, the PSF was found to be anisotropic.

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.

The detection of rolling bearing faults is essential to ensure the operational safety of rotating machinery. An effective method for diagnosing rolling bearing faults is the maximum second-order cyclostationarity blind deconvolution (CYCBD) method, which has the ability to extract weak fault periodic pulse features. However, blind deconvolution methods such as CYCBD often fail when composite bearing faults occur in the presence of strong background noise. To overcome this issue, an adaptive blind deconvolution (ABDD) method based on improved CYCBD is proposed. In this method, a finite impulse response (FIR) filter bank is constructed to cover the entire frequency band of the signal, enabling fault frequency segmentation. The improved CYCBD is then used to obtain a filter pattern that locks on the fault frequency. These filter patterns are arranged in descending order based on the correlation kurtosis (CK). The required filtering mode is selected according to the sorting mode, and a spectrum analysis is performed to extract fault features of single and compound faults in the bearing. Simulation and experimental results demonstrate that ABDD effectively extracts bearing composite fault features and outperforms classic feature decomposition and blind deconvolution methods in extracting single and composite fault features.

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.

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.

OBJECTIVE. The objective of our study was to investigate the impact of point-spread function (PSF) reconstruction and lesion size on 68Ga-tetraazacyclododecanetetraacetic acid-DPhe1-Tyr3-octreotate (DOTATATE) PET/CT quantitative parameters. MATERIALS AND METHODS. A total of 38 patients with 42 68Ga-DOTATATE PET/CT studies and 125 lesions were included. Scans were reconstructed with and without PSF modulation. For each lesion, the maximum standardized uptake value (SUVmax) and peak standardized uptake value (SUVpeak), metabolic tumor volume (MTV), total lesion somatostatin avidity, and tumor somatostatin receptor expression heterogeneity using the AUC method were measured. Intraclass correlation coefficient (ICC) and Bland-Altman analyses were used to compare PSF and non-PSF values. A subgroup analysis was performed to determine the impact of lesion size. RESULTS. Of the 125 lesions, 51 were in the liver, 31 in lymph nodes, 17 in bone, eight in pancreas, four in lung, and 14 in other sites. The ICCs between PSF and non-PSF values were excellent for SUVmax, SUVpeak, MTV, and total lesion somatostatin avidity (ICC = 0.97-0.99), and the ICC was good for tumor somatostatin receptor expression heterogeneity (ICC = 0.81). Comparison of PSF with non-PSF values showed a bias (mean percentage change ± SD) of 27.5% ± 14.7% for SUVmax, 15.5% ± 9.5% for SUVpeak, -18.6% ± 37.6% for MTV, 0.8% ± 28.1% for total lesion somatostatin avidity, and -7.1% ± 11.0% for tumor somatostatin receptor expression heterogeneity. Comparison of PSF with non-PSF values for lesions less than 2 cm (n = 75) showed corresponding biases greater than those for lesions 2 cm or larger (n = 50). CONCLUSION. PSF reconstruction effected higher values for SUVmax and SUVpeak, produced decreased values for tumor somatostatin receptor expression heterogeneity, and had a variable effect on MTV and total lesion somatostatin avidity depending on lesion size.

A blind deconvolution problem is newly stated with the following conditions: the point-spread function is band limited, both the object and the point-spread function are nonnegative, and the solution is to be a diffraction-limited object. A blind deconvolution method was developed that can easily be applied to problems in optics because of the conditions used. The performance of the method is investigated with computer simulations.

Imaging of pressure-sensitive paint (PSP) for pressure measurement on moving surfaces is problematic due to the movement of the object within the finite exposure time of the imager, resulting in the blurring of the blade edges. The blurring problem is particularly challenging when high-sensitivity PSP with a long lifetime is used, where the long luminescence time constant of exponential light decay following a burst of excitation light energy results in blurred images. One method to ameliorate this effect is image deconvolution using a point spread function (PSF) based on an estimation of the luminescent time constant. Prior implementations of image deconvolution for PSP deblurring have relied upon a spatially invariant time constant in order to reduce computational time. However, the use of an assumed value of time constant leads to errors in the point spread function, particularly when strong pressure gradients (which cause strong spatial gradients in the decay time constant) are involved. This work introduces an iterative method of image deconvolution, where a spatially variant PSF is used. The point-by-point PSF values are found in an iterative manner, since the time constant depends on the local pressure value, which can only be found from the reduced PSP data. The scheme estimates a super-resolved spatially varying blur kernel with sub-pixel resolution without filtering the blurred image, and then restores the image using classical iterative regularization tools. A kernel-free forward model has been used to generate test images with known pressure surface maps and a varying amount of noise to evaluate the applicability of this scheme in different experimental conditions. A spinning disk setup with a grazing nitrogen jet for producing strong pressure gradients has also been used to evaluate the scheme on a real-world problem. Results including the convergence history and the effect of a regularization-iteration count are shown, along with a comparison with the previous PSP deblurring method.

Owing to the limited size and imperfections of the optical components in a spectrometer, aberrations inevitably make their way into 2D multifibre spectral images in the Large Sky Area Multi-Object Fiber Spectroscopy Telescope (LAMOST), which leads to obvious spatial variation of the point spread functions (PSFs). However, if spatially variant PSFs are estimated directly, the large storage and intensive computational requirements result in the deconvolution spectrum extraction method becoming intractable. In this paper, we propose a novel method to solve the problem of spatial variation of the PSFs through image aberration correction. When CCD image aberrations are corrected, the convolution kernel can be approximated by only one spatially invariant PSF. Specifically, a novel method based on machine learning is proposed to calibrate the distorted spectral images. The method includes many techniques, such as total least squares (TLS) algorithm, self-supervised learning and multilayer feed-forward neural networksnetworks, and it makes use of a special training set sampling scheme combining 2D distortion features in a flat-field spectrum and calibration lamp spectrum. The calibration experiments on the LAMOST CCD images show that the proposed method is feasible. Furthermore, the spectrum extraction results before and after calibration are compared, and the experimental results show that the characteristics of the extracted 1D waveform are closer to those of an ideal optics system after image correction, and that the PSF of the corrected object spectrum estimated by the blind deconvolution method is nearly centrosymmetric, which indicates that our proposed method can significantly reduce the complexity of spectrum extraction and improve extraction accuracy.

We propose to use the blind deconvolution and its modification to extract the point spread function (PSF) of layered metamaterials from a SNOM measurement. The measurement results are processed using the blind deconvolution algorithm to reconstruct the real-valued non-coherent PSF, or using the modified blind deconvolution introduced in this paper to reconstruct the complex-valued coherent PSF. The two algorithms are tested in simulations with a layered metamaterial deposited on a thin metallic mask with test apertures. We show that the modified algorithm is capable of recovering the approximate shape of complex PSF with a sub-wavelength full width at half maximum from a measurement in which the apertures are larger than the wavelength.

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.

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.

A weighted total variation algorithm was proposed for solving some blind deconvolution problems,and then we got the existence of energy functional minimum and educed corresponding thermal flow.In computer simulations,the algorithm performs well even when we have no more accurate prior knowledge about point spread function and the original true image,besides some other constrains.Experiments show that the proposed algorithm is more effective and performs better than the total variation blind deconvolution method proposed.

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.

Over the past decade, scanning fluorescence microscopy based on two-photon excitation has become an important branch of microscopic bio-imaging. Compared to traditional scanning techniques, two-photon microscopy offers a number of distinct advantages. First, scanning of the point-like excitation spot used for imaging results in images with excellent axial depth discrimination. In addition, the limited extent of the excitation volume also limits specimen photo-damage to the focal volume. Finally, the long, near-infixed wavelengths used for sample excitation allow in-depth, non-invasive imaging of optically turbid biological samples. For in-depth imaging, the microscopic objective and often optically heterogeneous biological specimen forms a complex system. To optimize imaging quality in two-photon microscopy, an understanding of the point-spread-function (PSF) is essential. In this work, we attempted to characterize the two-photon PSF by two methods: direct imaging of 0.1 ym fluorescent microspheres and multicolor imaging of 2 ym green fluorescent microspheres in a uniform blue fluorescent background. In both measurements, the turbidity of the surrounding medium was varied by changing the concentration of Liposyn III, a scattering component in the specimen. We found that at discrete Liposyn III concentrations between 0 and 2%, the PSF widths were not affected by the amount of scatterers present. However, the imaged contrast continued to degrade as a function of the amount of scatter. This suggests that the broadening of the tail region of the PSF can be the cause of image contrast loss. We will also discuss the possibility of using blind- deconvolution as a method to obtain PSF information in complex biological specimen.