Reduced order strip Kalman filtering using singular perturbation method

Includes bibliographical references.Strip Kalman filtering for restoration of images degraded by linear shift invariant (LSI) blur and additive white Gaussian (WG) noise is considered. The image process is modeled by a 1-D vector autoregressive (AR) model in each strip. It is shown that the composite dynamic model that is obtained by combining the image model and the blur model takes the form of a singularly perturbed system owing to the strong-weak correlation effects within a window. The time scale property of the singularly perturbed system is then utilized to decompose the original system into reduced order subsystems which closely capture the behavior of the full order system. For these subsystems the relevant Kalman filtering equations are given which provide the suboptimal filtered estimates of the image and the one-step prediction estimates of the blur needed for the next stage. Simulation results are also provided

Two-dimensional block Kalman filtering for image restoration

Includes bibliographical references.This paper is concerned with developing an efficient two-dimensional (2-D) block Kalman filtering for digital image restoration. A new 2-D multiinput, multioutput (MIMO) state-space structure for modeling the image generation process is introduced. This structure is derived by arranging a vector autoregressive (AR) model with a causal quarter-plane region of support in block form. This model takes into account the correlations of the image data in successive neighboring blocks and, as a result, reduces the edge effects prominent in the available Kalman strip filtering techniques. The degradation model for an infinite extent Linear space invariant (LSI) blur and white Gaussian (WG) noise is also modeled by an MIMO block state-space equation stemmed from a single-input single-output (SISO) 2-D state-space structure. The image generation model and the degradation model are combined to yield a composite block-state dynamic structure. The block Kalman filtering equations are obtained for this dynamic structure and then used to compute the suboptimal filter estimates of a noisy and blurred image

Two-dimensional adaptive block Kalman filtering of SAR imagery

Includes bibliographical references.Speckle effects are commonly observed in synthetic aperture radar (SAR) imagery. In airborne SAR systems the effect of this degradation reduces the accuracy of detection substantially. Thus, the elimination of this noise is an important task in SAR imaging systems. In this paper a new method for speckle noise removal is introduced using 2-D adaptive block Kalman filtering (ABKF). The image process is represented by an autoregressive (AR) model with nonsymmetric half-plane (NSHP) region of support. New 2-D Kalman filtering equations are derived which take into account not only the effect of speckles as a multiplicative noise but also those of the additive receiver thermal noise and the blur. This method assumes local stationarity within a processing window, whereas the image can be assumed to be globally nonstationary. A recursive identification process using the stochastic Newton approach is also proposed which can be used on-line to estimate the filter parameters based upon the information within each new block of the image. Simulation results on several images are provided to indicate the effectiveness of the proposed method when used to remove the effects of speckle noise as well as that of the additive noise

Probabilistic modeling and inference for sequential space-varying blur identification

International audienceThe identification of parameters of spatially variant blurs given a clean image and its blurry noisy version is a challenging inverse problem of interest in many application fields, such as biological microscopy and astronomical imaging. In this paper, we consider a parametric model of the blur and introduce an 1D state-space model to describe the statistical dependence among the neighboring kernels. We apply a Bayesian approach to estimate the posterior distribution of the kernel parameters given the available data. Since this posterior is intractable for most realistic models, we propose to approximate it through a sequential Monte Carlo approach by processing all data in a sequential and efficient manner. Additionally, we propose a new sampling method to alleviate the particle degeneracy problem, which is present in approximate Bayesian filtering, particularly in challenging concentrated posterior distributions. The considered method allows us to process sequentially image patches at a reasonable computational and memory costs. Moreover, the probabilistic approach we adopt in this paper provides uncertainty quantification which is useful for image restoration. The practical experimental results illustrate the improved estimation performance of our novel approach, demonstrating also the benefits of exploiting the spatial structure the parametric blurs in the considered models

Linear Reconstruction of Non-Stationary Image Ensembles Incorporating Blur and Noise Models

Two new linear reconstruction techniques are developed to improve the resolution of images collected by ground-based telescopes imaging through atmospheric turbulence. The classical approach involves the application of constrained least squares (CLS) to the deconvolution from wavefront sensing (DWFS) technique. The new algorithm incorporates blur and noise models to select the appropriate regularization constant automatically. In all cases examined, the Newton-Raphson minimization converged to a solution in less than 10 iterations. The non-iterative Bayesian approach involves the development of a new vector Wiener filter which is optimal with respect to mean square error (MSE) for a non-stationary object class degraded by atmospheric turbulence and measurement noise. This research involves the first extension of the Wiener filter to account properly for shot noise and an unknown, random optical transfer function (OTF). The vector Wiener filter provides superior reconstructions when compared to the traditional scalar Wiener filter for a non-stationary object class. In addition, the new filter can provide a superresolution capability when the object\u27s Fourier domain statistics are known for spatial frequencies beyond the OTF cutoff. A generalized performance and robustness study of the vector Wiener filter showed that MSE performance is fundamentally limited by object signal-to-noise ratio (SNR) and correlation between object pixels

Adaptive Image Restoration: Perception Based Neural Nework Models and Algorithms.

Abstract This thesis describes research into the field of image restoration. Restoration is a process by which an image suffering some form of distortion or degradation can be recovered to its original form. Two primary concepts within this field have been investigated. The first concept is the use of a Hopfield neural network to implement the constrained least square error method of image restoration. In this thesis, the author reviews previous neural network restoration algorithms in the literature and builds on these algorithms to develop a new faster version of the Hopfield neural network algorithm for image restoration. The versatility of the neural network approach is then extended by the author to deal with the cases of spatially variant distortion and adaptive regularisation. It is found that using the Hopfield-based neural network approach, an image suffering spatially variant degradation can be accurately restored without a substantial penalty in restoration time. In addition, the adaptive regularisation restoration technique presented in this thesis is shown to produce superior results when compared to non-adaptive techniques and is particularly effective when applied to the difficult, yet important, problem of semi-blind deconvolution. The second concept investigated in this thesis, is the difficult problem of incorporating concepts involved in human visual perception into image restoration techniques. In this thesis, the author develops a novel image error measure which compares two images based on the differences between local regional statistics rather than pixel level differences. This measure more closely corresponds to the way humans perceive the differences between two images. Two restoration algorithms are developed by the author based on versions of the novel image error measure. It is shown that the algorithms which utilise this error measure have improved performance and produce visually more pleasing images in the cases of colour and grayscale images under high noise conditions. Most importantly, the perception based algorithms are shown to be extremely tolerant of faults in the restoration algorithm and hence are very robust. A number of experiments have been performed to demonstrate the performance of the various algorithms presented

Electronic Image Stabilization for Mobile Robotic Vision Systems

When a camera is affixed on a dynamic mobile robot, image stabilization is the first step towards more complex analysis on the video feed. This thesis presents a novel electronic image stabilization (EIS) algorithm for small inexpensive highly dynamic mobile robotic platforms with onboard camera systems. The algorithm combines optical flow motion parameter estimation with angular rate data provided by a strapdown inertial measurement unit (IMU). A discrete Kalman filter in feedforward configuration is used for optimal fusion of the two data sources. Performance evaluations are conducted by a simulated video truth model (capturing the effects of image translation, rotation, blurring, and moving objects), and live test data. Live data was collected from a camera and IMU affixed to the DAGSI Whegs™ mobile robotic platform as it navigated through a hallway. Template matching, feature detection, optical flow, and inertial measurement techniques are compared and analyzed to determine the most suitable algorithm for this specific type of image stabilization. Pyramidal Lucas-Kanade optical flow using Shi-Tomasi good features in combination with inertial measurement is the EIS algorithm found to be superior. In the presence of moving objects, fusion of inertial measurement reduces optical flow root-mean-squared (RMS) error in motion parameter estimates by 40%. No previous image stabilization algorithm to date directly fuses optical flow estimation with inertial measurement by way of Kalman filtering