Convolutional dictionary learning for blind deconvolution of optical coherence tomography images
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Fast Bayesian blind deconvolution with Huber Super Gaussian priors
We report expectation Maximization (EM) based inference has already proven to be a very powerful tool to solve blind image deconvolution (BID) problems. Unfortunately, three important problems still impede the application of EM in BID: the undesirable saddle points and local minima caused by highly nonconvex priors, the instability around zero of some of the most interesting sparsity promoting priors, and the intrinsic high computational cost of the corresponding BID algorithm. In this paper we first show how Super Gaussian priors can be made numerically tractable around zero by introducing the family of Huber Super Gaussian priors and then present a fast EM based blind deconvolution method formulated in the image space. In the proposed computational approach, image and kernel estimation are performed by using the Alternating Direction Method of Multipliers (ADMM), which allows to exploit the advantages of FFT computation. For highly nonconvex priors, we propose a Smooth ADMM (SADMM) approach to avoid poor BID estimates. In conclusion, extensive experiments demonstrate that the proposed method significantly outperforms state-of-the-art BID methods in terms of quality of the reconstructions and speed.
97 MATHEMATICS AND COMPUTING↗
Variable Projection Method for Semi-Blind Deconvolution with Mixed Gaussian Kernels
I am a summer intern. The thesis includes work I’ve done here this summer with EV40. It is on mathematical methods for deblurring images. It doesn't include any radiographic images or data, its all synthetic examples - Dworaczyk, Jordan T.
97 MATHEMATICS AND COMPUTING↗
Super Resolving Unrolled Neural Networks for Remote Sensing
In remote sensing systems, the capabilities of the system are constrained by the complex interactions between size, weight, and power (SWAP) of potential designs. In electro-optical (EO) systems, examples of these critical parameters include the system’s sensitivity and resolution. Those parameters can be increased by ever larger optical apertures and focal planes but at the cost of more SWAP. Multi-image super resolution (MISR) techniques allow resolution to be enhanced via computation rather than more sophisticated optical hardware. These algorithms combine multiple images together into a single, higher resolution image, trading temporal resolution and computation for spatial resolution. Fielded MISR techniques, such as Drizzle, can require several hundred images to create a single super resolved image, implying reduced temporal resolution, increased data acquisition load, and limiting mission applications. Iterative techniques, such as model-based image reconstruction and compressive sensing, have been shown to create super resolved images using fewer images than Drizzle. They do this by posing an optimization problem that balances accuracy between a highly accurate physical model and an image model. In the case of super resolution, the physical model is defined by the relation between low resolution input images and the desired high resolution output image. The image model encodes some assumptions about the super resolved image. These assumptions are meant to suppress reconstruction artifacts that arise due to deterministic physical model error, stochastic measurement noise, and potential undersampling. In practice, the performance of iterative methods are limited by imaging models compatible with optimization. Deep learning-based methods can effectively learn image models of arbitrary complexity, but lack the theoretical explainability and robustness of iterative techniques. Consensus equilibrium (CE) generalizes the iterative techniques beyond optimization, enabling blackbox algorithms such as traditional and neural image denoisers to be used as the image model. CE-based approaches retain much of the explainability and robustness of iterative techniques while allowing the expressiveness of machine learning image models to be used. Additionally, by unrolling iterations of CE with an embedded image denoiser, the image denoiser can be further trained and specialized to the specific application with potentially higher quality reconstructions. Under this project, we demonstrated the feasibility of training an unrolled neural network based upon CE. While we didn’t train one, we showed that the CE process is differentiable and its gradient can be tractably computed. We also explored the usage of a variants of CE akin to generative neural works. Most importantly, we applied the CE framework to a number of problems including non-blind deconvolution, upsampling, single-image super resolution, MISR, event-based sensing, and saturated deconvolution. Our MISR prototype creates high quality reconstructions with an order of magnitude fewer images than previous approaches and, critically, produces these reconstructions fast enough for practical usage.
47 OTHER INSTRUMENTATION↗
The Second Flight of the Sunrise Balloon-borne Solar Observatory: Overview of Instrument Updates, the Flight, the Data, and First Results
The Sunrise balloon-borne solar observatory, consisting of a 1 m aperture telescope that provides a stabilized image to a UV filter imager and an imaging vector polarimeter, carried out its second science flight in 2013 June. It provided observations of parts of active regions at high spatial resolution, including the first high-resolution images in the Mg ii k line. The obtained data are of very high quality, with the best UV images reaching the diffraction limit of the telescope at 3000 Å after Multi-Frame Blind Deconvolution reconstruction accounting for phase-diversity information. Here a brief update is given of the instruments and the data reduction techniques, which includes an inversion of the polarimetric data. Mainly those aspects that evolved compared with the first flight are described. A tabular overview of the observations is given. In addition, an example time series of a part of the emerging active region NOAA AR 11768 observed relatively close to disk center is described and discussed in some detail. The observations cover the pores in the trailing polarity of the active region, as well as the polarity inversion line where flux emergence was ongoing and a small flare-like brightening occurred in the course of the time series. The pores are found to contain magnetic field strengths ranging up to 2500 G, and while large pores are clearly darker and cooler than the quiet Sun in all layers of the photosphere, the temperature and brightness of small pores approach or even exceed those of the quiet Sun in the upper photosphere.
79 ASTRONOMY AND ASTROPHYSICS↗
Variational Dirichlet Blur Kernel Estimation
Blind image deconvolution involves two key objectives: 1) latent image and 2) blur estimation. For latent image estimation, we propose a fast deconvolution algorithm, which uses an image prior of nondimensional Gaussianity measure to enforce sparsity and an undetermined boundary condition methodology to reduce boundary artifacts. For blur estimation, a linear inverse problem with normalization and nonnegative constraints must be solved. However, the normalization constraint is ignored in many blind image deblurring methods, mainly because it makes the problem less tractable. In this paper, we show that the normalization constraint can be very naturally incorporated into the estimation process by using a Dirichlet distribution to approximate the posterior distribution of the blur. Making use of variational Dirichlet approximation, we provide a blur posterior approximation that considers the uncertainty of the estimate and removes noise in the estimated kernel. Furthermore, experiments with synthetic and real data demonstrate that the proposed method is very competitive to the state-of-the-art blind image restoration methods.
97 MATHEMATICS AND COMPUTING↗
Scatter and Blur Corrections for High-Energy X-Ray Radiography
High-energy X-ray radiography is useful as a highly penetrating method for imaging through dense materials. However, the primary modes of interaction of X-rays at these energies involve scattering or the production of secondary high-energy photons, which can interfere with the image. In addition, detector blurring, often resulting from scatter within the detector, can reduce image sharpness. Both of these processes can be mitigated with the use of convolution kernels, with the main challenge being that the proper kernel to use is not known, particularly for the scatter contribution. By radiographing solid slabs of uniform attenuation, we show that point spread functions and material-specific point scatter functions can be determined to significantly reduce the effect of detector blurring and object scatter. Constraining the fits to the slabs and uniform transmission within the slabs is sufficient to recover these functions. A functional form that reproduces the angular distribution of high-energy bremsstrahlung X-rays is presented for recovering point scatter functions. In conclusion, the method is applied to radiographs of objects from bremsstrahlung X-ray sources operating at 4- and 7.5-MV endpoint energies and a significant increase in sharpness is observed.
Blind deconvolution↗