Direction of arrival estimation using parametric signal models

We consider the problem of estimating the directions-of-arrival (DOAs) of narrowband sources with known center frequency. The paper evaluates the potential improvement in estimation accuracy by using spatial-temporal processing for signals obeying a deterministic parametric model. One would expect that prior information about the temporal structure of the signals will yield some gain in performance. By deriving the Cramer-Rao bound (CRB) on the DOA estimates, we quantify this gain and identify the cases for which the gain is significant. We show that for the single-source case, spatial-temporal processing does not yield any gain in performance relative to conventional spatial processing. For multiple noncoherent signals, incorporating temporal processing can achieve the single-source performance, yielding a significant gain for the case of multiple sources with small spatial separation relative to the beamwidth of the array. However, spatial-temporal processing cannot yield any gain in performance for multiple coherent signals     

Lower bounds for parametric estimation with constraints

A Chapman-Robbins form of the Barankin bound is used to derive a multiparameter Cramer-Rao (CR) type lower bound on estimator error covariance when the parameter &thetas;∈Rⁿ is constrained to lie in a subset of the parameter space. A simple form for the constrained CR bound is obtained when the constraint set Θ_C, can be expressed as a smooth functional inequality constraint. It is shown that the constrained CR bound is identical to the unconstrained CR bound at the regular points of Θ_C, i.e. where no equality constraints are active. On the other hand, at those points &thetas;∈Θ_C where pure equality constraints are active the full-rank Fisher information matrix in the unconstrained CR bound must be replaced by a rank-reduced Fisher information matrix obtained as a projection of the full-rank Fisher matrix onto the tangent hyperplane of the full-rank Fisher matrix onto the tangent hyperplane of the constraint set at &thetas;. A necessary and sufficient condition involving the forms of the constraint and the likelihood function is given for the bound to be achievable, and examples for which the bound is achieved are presented. In addition to providing a useful generalization of the CR bound, the results permit analysis of the gain in achievable MSE performance due to the imposition of particular constraints on the parameter space without the need for a global reparameterization     

Nonlinear image estimation using piecewise and local image models

We introduce a new approach to image estimation based on a flexible constraint framework that encapsulates meaningful structural image assumptions. Piecewise image models (PIMs) and local image models (LIMs) are defined and utilized to estimate noise-corrupted images, PIMs and LIMs are defined by image sets obeying certain piecewise or local image properties, such as piecewise linearity, or local monotonicity. By optimizing local image characteristics imposed by the models, image estimates are produced with respect to the characteristic sets defined by the models. Thus, we propose a new general formulation for nonlinear set-theoretic image estimation. Detailed image estimation algorithms and examples are given using two PIMs: piecewise constant (PICO) and piecewise linear (PILI) models, and two LIMs: locally monotonic (LOMO) and locally convex/concave (LOCO) models. These models define properties that hold over local image neighborhoods, and the corresponding image estimates may be inexpensively computed by iterative optimization algorithms. Forcing the model constraints to hold at every image coordinate of the solution defines a nonlinear regression problem that is generally nonconvex and combinatorial. However, approximate solutions may be computed in reasonable time using the novel generalized deterministic annealing (GDA) optimization technique, which is particularly well suited for locally constrained problems of this type. Results are given for corrupted imagery with signal-to-noise ratio (SNR) as low as 2 dB, demonstrating high quality image estimation as measured by local feature integrity, and improvement in SNR.     

Video super resolution based on non-local regularization and reliable motion estimation

Video super-resolution (SR) is a process for reconstructing high-resolution (HR) images by utilizing complementary information among multiple low-resolution (LR) images. Accurate estimation of the motion among the LR images significantly affects the quality of the reconstructed HR image. In this paper, we analyze the possible reasons for the inaccuracy of motion estimation and then propose a multi-lateral filter to regularize the process of motion estimation. This filter can adaptively correct motion estimation according to the estimation reliability, image intensity discontinuity, and motion dissimilarity. Furthermore, we introduce a non-local prior to solve the ill-posed problem of HR image reconstruction. This prior can fully utilize the self-similarities existing in natural images to regularize the HR image reconstruction. Finally, we employ a Bayesian formulation to incorporate the two regularizations into one Maximum a Posteriori (MAP) estimation model, where the HR image and the motion estimation can be refined progressively in an alternative and iterative manner. In addition, an algorithm that estimates the blur kernel by analyzing edges in an image is also presented in this paper. Experimental results demonstrate that the proposed approaches are highly effective and compare favorably to state-of-the-art SR algorithms.     

Characterization of cell deformation and migration using a parametric estimation of image motion

This paper deals with the spatio-temporal analysis of two-dimensional deformation and motion of cells from time series of digitized video images. A parametric motion approach based on an affine model has been proposed for the quantitative characterization of cellular movements in different experimental areas of cellular biology including spontaneous cell deformation, cell mitosis, individual cell migration and collective migration of cell populations as cell monolayer. The accuracy and robustness of the affine model parameter estimation, which is based on a multiresolution algorithm, has been established from synthesized image sequences. A major interest of our approach is to follow with time the evolution of a few number of parameters characteristic of cellular motion and deformation. From the time-varying eigenvalues of the affine model square matrix, a precise quantification of the cell pseudopodial activity, as well as of cell division has been performed. For migrating cells, the motion quantification confirms that cell body deformation has a leading role in controlling nucleus displacement, the nucleus itself undergoing a larger rotational motion. At the cell population level, image motion analysis of in vitro wound healing experiments quantifies the heterogeneous cell populations dynamics.     

Estimating volumetric motion in human thorax with parametric matching constraints

In radiotherapy (RT), organ motion caused by breathing prevents accurate patient positioning, radiation dose, and target volume determination. Most of the motion-compensated trial techniques require collaboration of the patient and expensive equipment. Estimating the motion between two computed tomography (CT) three-dimensional scans at the extremes of the breathing cycle and including this information in the RT planning has been shyly considered, mainly because that is a tedious manual task. This paper proposes a method to compute in a fully automatic fashion the spatial correspondence between those sets of volumetric CT data. Given the large ambiguity present in this problem, the method aims to reduce gradually this uncertainty through two main phases: a similarity-parametrization data analysis and a projection-regularization phase. Results on a real study show a high accuracy in establishing the spatial correspondence between both sets. Embedding this method in RT planning tools is foreseen, after making some suggested improvements and proving the validity of the two-scan approach.     

Coordinate-descent super-resolution and registration for parametric global motion models

We present a method for simultaneously obtaining registration and super-resolution from a sequence of low resolution images, based on a coordinate-descent approach. The novelty of the algorithm resides on the registration step, which can be applied easily to any parametric global motion model. We prove the validity of the model with synthetic and real data experiments, being of special interest the good performance achieved in the difficult case of images registered under a projective transformation.     

Sub-pixel motion estimation using kernel methods

Modern video codecs such as MPEG2, MPEG4-ASP and H.264 depend on sub-pixel motion estimation to optimise rate-distortion efficiency. Sub-pixel motion estimation is implemented within these standards using interpolated values at 1/2 or 1/4 pixel accuracy. By using these interpolated values, the residual energy for each predicted macroblock is reduced. However this leads to a significant increase in complexity at the encoder, especially for H.264, where the cost of an exhaustive set of macroblock segmentations needs to be estimated for optimal mode selection. This paper presents a novel scheme for sub-pixel motion estimation based on the whole-pixel SAD distribution. Both half-pixel and quarter-pixel searches are guided by a model-free estimation of the SAD surface using a two dimensional kernel method. While giving an equivalent rate distortion performance, this approach approximately halves the number of quarter-pixel search positions giving an overall speed up of approximately 10% compared to the EPZS quarter-pixel method (the state of the art H.264 optimised sub-pixel motion estimator).     

Image motion estimation algorithms using cumulants

A class of algorithms is presented that estimates the displacement vector from two successive image frames consisting of signal plus noise. In the model, the signals are assumed to be either non-Gaussian or (quasistationary) deterministic; and, via a consistency result for cumulant estimators, the authors unify the stochastic and deterministic signal viewpoints. The noise sources are assumed to be Gaussian (perhaps spatially and temporally correlated) and of unknown covariance. Viewing image motion estimation as a 2D time delay estimation problem, the displacement vector of a moving object is estimated by solving linear equations involving third-order auto-cumulants and cross-cumulants. Additionally, a block-matching algorithm is developed that follows from a cumulant-error optimality criterion. Finally, the displacement vector for each pel is estimated using a recursive algorithm that minimizes a mean 2D fourth-order cumulant criterion. Simulation results are presented and discussed.     

A fast parametric motion estimation algorithm with illumination and lens distortion correction

Methods for estimating motion in video sequences that are based on the optical flow equation (OFE) assume that the scene illumination is uniform and that the imaging optics are ideal. When these assumptions are appropriate, these methods can be very accurate, but when they are not, the accuracy of the motion field drops off accordingly. This paper extends the models upon which the OFE methods are based to include irregular, time-varying illumination models and models for imperfect optics that introduce vignetting, gamma, and geometric warping, such as are likely to be found with inexpensive PC cameras. The resulting optimization framework estimates the motion parameters, illumination parameters, and camera parameters simultaneously. In some cases these models can lead to nonlinear equations which must be solved iteratively; in other cases, the resulting optimization problem is linear. For the former case an efficient, hierarchical, iterative framework is provided that can be used to implement the motion estimator.     

Maximum a posteriori estimation for SPECT using regularization techniques on massively parallel computers

Single photon emission computed tomography (SPECT) reconstructions performed using maximum a posteriori (penalized likelihood) estimation with the expectation maximization algorithm are discussed. Due to the large number of computations, the algorithms were performed on a massively parallel single-instruction multiple-data computer. Computation times for 200 iterations, using I.J. Good and R.A. Gaskins's (1971) roughness as a rotationally invariant roughness penalty, are shown to be on the order of 5 min for a 64x64 image with 96 view angles on an AMT-DAP 4096 processor machine and 1 min on a MasPar 4096 processor machine. Computer simulations performed using parameters for the Siemens gamma camera and clinical brain scan parameters are presented to compare two regularization techniques-regularization by kernel sieves and penalized likelihood with Good's rotationally invariant roughness measure-to filtered backprojection. Twenty-five independent sets of data are reconstructed for the pie and Hoffman brain phantoms. The average variance and average deviation are examined in various areas of the brain phantom. It is shown that while the geometry of the area examined greatly affects the observed results, in all cases the reconstructions using Good's roughness give superior variance and bias results to the two alternative methods.     

Nonuniform image motion estimation using Kalman filtering

This correspondence presents a new pixel-recursive algorithm for estimating the nonuniform image motion from noisy measurements. The proposed method is performed in two steps. First, the pixels are examined to identify the (detectable) moving pixels, using a binary hypothesis testing. Then, characterizing the motion of the identified moving pixels in terms of a unitary transformation, the motion coefficients are estimated using a Kalman filter. Because the motion vector is typically (spatially) slowly varying, the size of the motion coefficient vector is significantly reduced. Consequently, the proposed Kalman filter need only search for the truncated coefficients of the motion field. The proposed method is simulated on a computer, and results are compared with the algorithm reported by Netravali and Robbins (see Bell Syst. Tech. J. vol.58, no.3, p.631-70, Mar. 1979).     

Glacier motion estimation using SAR offset-tracking procedures

Two image-to-image patch offset techniques for estimating feature motion between satellite synthetic aperture radar (SAR) images are discussed. Intensity tracking, based on patch intensity cross-correlation optimization, and coherence tracking, based on patch coherence optimization, are used to estimate the movement of glacier surfaces between two SAR images in both slant-range and azimuth direction. The accuracy and application range of the two methods are examined in the case of the surge of Monacobreen in Northern Svalbard between 1992 and 1996. Offset-tracking procedures of SAR images are an alternative to differential SAR interferometry for the estimation of glacier motion when differential SAR interferometry is limited by loss of coherence, i.e. in the case of rapid and incoherent flow and of large acquisition time intervals between the two SAR images. In addition, an offset-tracking procedure in the azimuth direction may be combined with differential SAR interferometry in the slant-range direction in order to retrieve a two-dimensional displacement map when SAR data of only one orbit configuration are available.     

Fast motion estimation using bidirectional gradient methods

Gradient-based motion estimation methods (GMs) are considered to be in the heart of state-of-the-art registration algorithms, being able to account for both pixel and subpixel registration and to handle various motion models (translation, rotation, affine, and projective). These methods estimate the motion between two images based on the local changes in the image intensities while assuming image smoothness. This paper offers two main contributions. The first is enhancement of the GM technique by introducing two new bidirectional formulations of the GM. These improve the convergence properties for large motions. The second is that we present an analytical convergence analysis of the GM and its properties. Experimental results demonstrate the applicability of these algorithms to real images.     

A dynamic search pattern motion estimation algorithm using prioritized motion vectors

Motion estimation is one of the critical parts in video compression standards with a high computational load. Many motion estimation algorithms have been developed to reduce the number of search points compared to a full-search algorithm without losing the quality considerably. Most of them use fixed search patterns in their first step which may suffer from trapping into local minima or searching unnecessary blocks due to inappropriate size and type of search patterns. In this paper, a new dynamic search pattern using motion vectors of spatial and temporal neighboring blocks is proposed. The motion vectors of neighboring blocks are prioritized, in order to efficiently use of halfway stop technique. The simulation results indicate that proposed algorithm is very close to the full-search algorithm in quality, compared to other rivals. Moreover, the average number of searches is often less than other algorithms.     

Topology preserving deformable image matching using constrainedhierarchical parametric models

In this paper, we address the issue of topology preservation in deformable image matching. A novel constrained hierarchical parametric approach is presented, that ensures that the mapping is globally one-to one and thus preserves topology in the deformed image. The transformation between the source and target images is parameterized at different scales, using a decomposition of the deformation vector field over a sequence of nested (multiresolution) subspaces. The Jacobian of the mapping is controlled over the continuous domain of the transformation, ensuring actual topology preservation on the whole image support. The resulting fast nonlinear constrained optimization algorithm enables to track large nonlinear deformations while preserving the topology. Experimental results are presented both on simulated data and on real medical images.     

MSE-based regularization approach to direction estimation ofcoherent narrowband signals using linear prediction

This paper addresses the problem of directions of arrival (DOAs) estimation of coherent narrowband signals impinging on a uniform linear array (ULA) when the number of signals is unknown. By using an overdetermined linear prediction (LP) model with a subarray scheme, the DOAs of coherent signals can be estimated from the zeros of the corresponding prediction polynomial. Although the corrected least squares (CLS) technique can be used to improve the accuracy of the LP parameters estimated from the noisy array data, the inversion of the resulting matrix in the CLS estimation is ill-conditioned, and then, the CLS estimation becomes unstable. To combat this numerical instability, we introduce multiple regularization parameters into the CLS estimation and show that determining the number of coherent signals is closely related to the truncation of the eigenvalues. An analytical expression of the mean square error (MSE) of the estimated LP parameters is derived, and it is clarified that the number of signals can be determined by comparing the optimal regularization parameters with the corresponding eigenvalues. An iterative regularization algorithm is developed for estimating directions without any a priori knowledge, where the number of coherent signals and the noise variance are estimated from the noise-corrupted received data simultaneously     

Frequency-domain motion estimation using a complex lapped transform

A frequency-domain algorithm for motion estimation based on overlapped transforms of the image data is developed as an alternative to block matching methods. The complex lapped transform (CLT) is first defined by extending the lapped orthogonal transform (LOT) to have complex basis functions. The CLT basis functions decay smoothly to zero at their end points, and overlap by 2:1 when a data sequence is transformed. A method for estimating cross-correlation functions in the CLT domain is developed. This forms the basis of a motion estimation algorithm that calculates vectors for overlapping, windowed regions of data. The overlapping data window used has no block edge discontinuities and results in smoother motion fields. Furthermore, when motion compensation is performed using similar overlapping regions, the algorithm gives comparable or smaller prediction errors than standard models using exhaustive search block matching, and computational load is lower for larger displacement ranges and block sizes.     

Efficient tree structured motion estimation using successive elimination

In H.264/AVC, tree structured motion estimation enhances the coding efficiency significantly while dramatically increasing the computational complexity of block matching. In the paper, a successive elimination algorithm (SEA) is implemented in tree structured motion estimation with a simple and effective method to determine the initial motion vector, which exploits the strong correlation among the partially overlapped variable-size blocks. With identical performance to a full search algorithm, computations for block matching can be reduced to 1%-20%. Further, the SEA can be improved by incorporating two early termination conditions, then named 'Quick SEA'. Finally, a novel fast motion estimation algorithm, successive elimination diamond search (SEDS), is proposed by efficiently integrating the Quick SEA and a modified diamond search pattern. Simulation results show that the proposed Quick SEA can reduce the computational complexity of block matching by 3-5 times compared to the basic SEA. SEDS further reduces by about one-half the computations of Quick SEA. With similar rate distortion performance, 0.2%-1% block matching distortion is calculated for SEDS with corresponding speed-up factors of 100 to 500 in comparison with the full search algorithm.     

Generalised block-matching motion estimation using quad-treestructured spatial decomposition

A generalised block-matching motion estimation with variable-size blocks is proposed. The location and size of each block are determined from a quad-tree spatial decomposition algorithm. Experimental results with head-and-shoulders test image sequences show that motion-compensated errors with this method have lower entropy than the conventional fixed or variable-size block-matching techniques. The quality of the coded pictures under the proposed method with an H.261 codec, both subjectively and in terms of PSNR, outperforms the conventional use of fixed and variable block-size motion estimators