Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data

The ubiquity of integrating detectors in imaging and other applications implies that a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of interest. In this article, we first show how the so-called Skellam distribution arises from the fact that Haar wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of Poisson counts. We then provide two main theorems on Skellam shrinkage, one showing the near-optimality of shrinkage in the Bayesian setting and the other providing for unbiased risk estimation in a frequentist context. These results serve to yield new estimators in the Haar transform domain, including an unbiased risk estimate for shrinkage of Haar-Fisz variance-stabilized data, along with accompanying low-complexity algorithms for inference. We conclude with a simulation study demonstrating the efficacy of our Skellam shrinkage estimators both for the standard univariate wavelet test functions as well as a variety of test images taken from the image processing literature, confirming that they offer substantial performance improvements over existing alternatives.Comment: 27 pages, 8 figures, slight formatting changes; submitted for publicatio

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

A Video Stabilization Method Based on Inter-frame Image Matching Scorea

Video stabilization is an important video enhancement technology which aims at removing annoying shaky motion from videos. In this paper, we propose an robust and efficient video stabilization algorithm based on inter-frame image matching score. Firstly, image matching is performed by a method combining Maximally Stable Extremal Regions (MSERs) detection algorithm and Features from Accelerated Segment Test (FAST) corner detection algorithm, which can get the matching score and the motion parameters of the frame image. Then, the matching score is filtered to filter out the high frequency component and keep the low frequency component. And the motion compensation is performed on the current frame image according to the ratio of the matching score before and after the filtering to retain the global motion and remove the local jitter. Various classical corner detection operators and region matching operators are compared in experiments. And experimental results illustrate that the proposed method is effective to stabilize translational, rotational, and zooming jitter and robust to local motions, and has the state-of-the-art processing speed to meet the needs of real-time equipment

Discrete-wavelet-transform recursive inverse algorithm using second-order estimation of the autocorrelation matrix

The recursive-least-squares (RLS) algorithm was introduced as an alternative to LMS algorithm with enhanced performance. Computational complexity and instability in updating the autocolleltion matrix are some of the drawbacks of the RLS algorithm that were among the reasons for the intrduction of the second-order recursive inverse (RI) adaptive algorithm. The 2nd order RI adaptive algorithm suffered from low convergence rate in certain scenarios that required a relatively small initial step-size. In this paper, we propose a newsecond-order RI algorithm that projects the input signal to a new domain namely discrete-wavelet-transform (DWT) as pre step before performing the algorithm. This transformation overcomes the low convergence rate of the second-order RI algorithm by reducing the self-correlation of the input signal in the mentioned scenatios. Expeirments are conducted using the noise cancellation setting. The performance of the proposed algorithm is compared to those of the RI, original second-order RI and RLS algorithms in different Gaussian and impulsive noise environments. Simulations demonstrate the superiority of the proposed algorithm in terms of convergence rate comparedto those algorithms

Hyperbolic Wavelet-Fisz denoising for a model arising in Ultrasound Imaging

International audienceWe present an algorithm and its fully data-driven extension for noise reduction in ultrasound imaging. Our proposed method computes the hyperbolic wavelet transform of the image, before applying a multiscale variance stabilization technique, via a Fisz transformation. This adapts the wavelet coefficients statistics to the wavelet thresholding paradigm. The aim of the hyperbolic setting is to recover the image while respecting the anisotropic nature of structural details. The data-driven extension removes the need for any prior knowledge of the noise model parameters by estimating the noise variance using an isotonic Nadaraya-Watson estimator. Experiments on synthetic and real data, and comparisons with other noise reduction methods demonstrate the potential of our method at recovering ultrasound images while preserving tissue details. Finally, we emphasize the noise model we consider by applying our variance estimation procedure on real images

Measurements, Models, Systems and Design

531 s.