We propose EMORe, an adaptive reconstruction method designed to enhance motion robustness in free-running, free-breathing self-gated 5D cardiac magnetic resonance imaging (MRI). Traditional self-gating-based motion binning for 5D MRI often results in residual motion artifacts due to inaccuracies in cardiac and respiratory signal extraction and sporadic bulk motion, compromising clinical utility. EMORe addresses these issues by integrating adaptive inter-bin correction and explicit outlier rejection within an expectation-maximization (EM) framework, whereby the E-step and M-step are executed alternately until convergence. In the E-step, probabilistic (soft) bin assignments are refined by correcting misassignment of valid data and rejecting motion-corrupted data to a dedicated outlier bin. In the M-step, the image estimate is improved using the refined soft bin assignments. Validation in a simulated 5D MRXCAT phantom demonstrated EMORe’s superior performance compared to standard compressed sensing reconstruction, showing significant improvements in peak signal-to-noise ratio, structural similarity index, edge sharpness, and bin assignment accuracy across varying levels of simulated bulk motion. In vivo validation in 13 volunteers further confirmed EMORe’s robustness, significantly enhancing blood-myocardium edge sharpness and reducing motion artifacts compared to compressed sensing, particularly in scenarios with controlled coughing-induced motion. Although EMORe incurs a modest increase in computational complexity, its adaptability and robust handling of bulk motion artifacts improves image quality, supporting its potential for improved clinical applicability and diagnostic confidence of 5D cardiac MRI.

We consider the maximum likelihood (ML) parameter estimation problem for mixed integer linear models with arbitrary noise covariance. This problem appears in applications such as single frequency estimation, phase contrast imaging, and direction of arrival (DoA) estimation. Parameter estimates are found by solving a closest lattice point problem, which requires a lattice basis. In this letter, we present a lattice basis construction for ML parameter estimation and conclude with simulated results from DoA estimation and phase contrast imaging.

Nonuniform array geometries provide freedom for increased aperture and reduced mutual coupling. A necessary and sufficient condition is given for an array of isotropic sensor elements to be unambiguous for any specified set of directions of arrival. The set of unambiguous spatial frequencies is shown to be a parallelepiped, admitting simple geometrical interpretation. Results are used in design of linear, planar, and 3D arrays.

Coherent imaging systems such as synthetic aperture radar (SAR) are subject to speckle, the reduction of which is an active area of study. Methods based on deep convolutional neural networks (CNNs) have recently demonstrated state-of-the-art performance in the removal of additive noise from natural images and speckle from single-channel SAR images. The application of deep learning to multichannel SAR modalities such as polarimetric SAR (PolSAR) is complicated in part by the nature of the data as images of complex-valued covariance matrices. In this article, we propose a CNN-based PolSAR despeckling approach that uses an invertible transformation involving a matrix logarithm to facilitate CNN processing of the PolSAR data. A residual learning strategy is adopted, in which the CNN is trained to identify the speckle component which is then removed from the corrupted image. The experimental results on simulated and measured PolSAR data show the proposed approach to markedly reduce speckle and preserve scene features.

In phase-contrast magnetic resonance imaging (PC-MRI), spin velocity contributes to the phase measured at each voxel. Therefore, estimating velocity from potentially wrapped phase measurements is the task of solving a system of noisy congruence equations. We propose Phase Recovery from Multiple Wrapped Measurements (PRoM) as a fast, approximate maximum likelihood estimator of velocity from multi-coil data with possible amplitude attenuation due to dephasing. The estimator can recover the fullest possible extent of unambiguous velocities, which can greatly exceed twice the highest venc. The estimator uses all pairwise phase differences and the inherent correlations among them to minimize the estimation error. Correlations are directly estimated from multi-coil data without requiring knowledge of coil sensitivity maps, dephasing factors, or the actual per-voxel signal-to-noise ratio. Derivation of the estimator yields explicit probabilities of unwrapping errors and the probability distribution for the velocity estimate; this, in turn, allows for optimized design of the phase-encoded acquisition. These probabilities are also incorporated into spatial post-processing to further mitigate wrapping errors. Simulation, phantom, and in vivo results for three-point PC-MRI acquisitions validate the benefits of reduced estimation error, increased recovered velocity range, optimized acquisition, and fast computation. A phantom study at 1.5T demonstrates 48.5% decrease in root mean squared error using PRoM with post-processing versus a conventional "dual-venc" technique. Simulation and 3T in vivo results likewise demonstrate the proposed benefits.

The covariance matrix estimation problem is posed in both the Bayesian and frequentist settings as the solution of a maximum a posteriori (MAP) or maximum likelihood (ML) optimization, respectively, when the true covariance consists of a known (or bounded) noise floor and a low-rank component. Persymmetric structure may also be assumed. The MAP and ML solutions with the non-convex rank constraint are shown to be a simple scalar thresholding of eigenvalues of a suitably translated and projected sample covariance matrix. No iterative optimization is required; therefore, the computation is suited to real-time applications. Our proof is short and elementary without resorting to the duality theory. Numerical results are presented to illustrate the improved estimation performance obtained by incorporating the structural constraints on the unknown covariance.

In this work, we present a novel technique for image recovery from highly undersampled phase contrast magnetic resonance imaging (PC-MRI) data. Our approach is holistic and includes modeling of the underlying physics, optimized sampling strategies, and design of a novel inversion algorithm. We capture the unique magnitude and phase structure of PC-MRI data as a non-Gaussian conditional mixture density. We then create a factor graph that describes the joint posterior probability of the inference variables given the noisy measurements. A combination of standard belief propagation and generalized approximate message passing (GAMP) is used to form an iterative inversion algorithm capable of producing MAP or MMSE estimates of the signal of interest. Using the proposed technique, we demonstrate high-fidelity PC-MRI recovery for simulated and phantom data undersampled by a factor of ten.

A nested uniform sampling over the sphere is presented. The set of sampling points contains a sequence of nested subsets, each providing an approximately uniform covering of the sphere. The proposed Matryoshka covering of the sphere allows multiresolution 3-D imaging. Simulation and electron paramagnetic resonance imaging results illustrate its application to 3-D tomography.

Remote sensing with radar is typically an ill-posed linear inverse problem: a scene is to be inferred from limited measurements of scattered electric fields. Parsimonious models provide a compressed representation of the unknown scene and offer a means for regularizing the inversion task. The emerging field of compressed sensing combines nonlinear reconstruction algorithms and pseudorandom linear measurements to provide reconstruction guarantees for sparse solutions to linear inverse problems. This paper surveys the use of sparse reconstruction algorithms and randomized measurement strategies in radar processing. Although the two themes have a long history in radar literature, the accessible framework provided by compressed sensing illuminates the impact of joining these themes. Potential future directions are conjectured both for extension of theory motivated by practice and for modification of practice based on theoretical insights.

The performance of four algorithms for detecting the presence of pulsed sinusoidal interference in microwave radiometry is compared. The pulsed sinusoidal interference sources considered have unknown frequency, initial phase, amplitude, arrival time, and duration. The statistical properties of three of the algorithms are determined analytically, although numerical integrations are required in some cases in order to compute the obtained probabilities of detection. The performance of the fourth algorithm is evaluated using Monte Carlo procedures. Results show that three of the algorithms have a performance that is roughly comparable for the cases considered, while the fourth yields reduced sensitivity. A more detailed study of two of the algorithms, a simple energy detector called the pulse detection algorithm and a ldquopeakrdquo picking detector based on the use of data spectrograms, is also provided.

The performance of four algorithms for detecting the presence of short pulsed sinusoidal interference in microwave radiometry is compared. The pulsed sinusoidal interference sources considered have unknown frequency, initial phase, amplitude, arrival time, and duration. Statistical properties of three of the algorithms can be determined analytically, although numerical integrations are required in some cases in order to compute the obtained probabilities of detection. The performance of the fourth algorithm was evaluated using Monte Carlo procedures. Results show that three of the algorithms have a performance that is roughly comparable for the cases considered, while the fourth yields reduced sensitivity.

Sensor location information is a prerequisite to the utility of most sensor networks. In this paper we present a robust and low-complexity algorithm to self-localize and orient sensors in a network based on angle-of-arrival (AOA) information. The proposed non-iterative subspace-based method is robust to missing and noisy measurements and works for cases when sensor orientations are either known or unknown. We show that the computational complexity of the algorithm is O (mn2), where m is the number of measurements and n is the total number of sensors. Simulation results demonstrate that the error of the proposed subspace algorithm is only marginally greater than an iterative maximum-likelihood estimator (MLE), while the computational complexity is two orders of magnitude less. Additionally, the iterative MLE is prone to converge to local maxima in the likelihood function without accurate initialization. We illustrate that the proposed subspace method can be used to initialize the MLE and obtain near-Cramér-Rao performance for sensor localization. Finally, the scalability of the subspace algorithm is illustrated by demonstrating how clusters within a large network may be individually localized and then merged.

Distributed sensing systems fuse information from various local measurements to form joint estimates of physical phenomena. We study Bayesian parameter estimation with measurement failures, where the probability of failing to make an observation depends on the unknown parameters. Both the absence and the existence of the measurements provide information about the parameters. We present lower bounds for minimum mean square error estimation. The bounds are applied to the analysis of sensor arrays for source localization and the distributed estimation problem with binary detectors.

Due to inherent factors such as a small and fragmented market and rapid hardware obsolescence, the conventional textbook is inadequate for DSP laboratory education. Freely available open-content materials that enable and promote both local customization and further development by a community of educators offers a fresh approach to lab text development that can surmount these barriers. We overview a joint effort under the aegis of the Connexions Project to develop a large pool of DSP lab modules sufficient to serve as the complete, stand-alone text for several types of DSP lab courses.

The problem of computing exact finite impulse response (FIR) inverses for multivariate multiple-input multiple-output (MIMO) FIR systems is considered. Necessary and sufficient conditions for invertibility are given, along with computation techniques. Random systems and structured systems are defined. Necessary and sufficient conditions for the almost sure invertibility of structured random systems are derived. Bounds on the orders of the inverse filters are computed.

Connexions is a new approach to authoring, teaching, and learning that aims to fully exploit modern information technology. Available free of charge to anyone under open-content and open-source licenses, Connexions offers custom-tailored, current course material, is adaptable to a wide range of learning styles, and encourages students to explore the links among courses and disciplines. In contrast to the traditional process of textbook writing and publishing, Connexions fosters world-wide, cross-institution communities of authors, instructors, and students, who collaboratively and dynamically fashion “modules” from which courses are constructed. We believe the ideas and philosophy embodied by Connexions have the potential to change the very nature of textbook writing and publishing, producing a dynamic, interconnected educational environment that is pedagogically sound, both time and cost efficient, and fun. This paper overviews the philosophy and technology behind Connexions and describes a nascent community developing material for DSP education.

A necessary and sufficient condition is given for the existence of a polynomial left inverse for a polynomial (FIR) system. Additionally, random systems are defined, and a sufficient condition is given for almost sure existence of a polynomial inverse. The two results extend previous work in single-input, multiple-output systems to the case of multiple input systems and to functions of several variables. An algorithm to compute minimal order equalizers is also presented. Corollaries describe calibration of polarimetric, wide-band radar imagery.

A Bayesian approach is presented for model-based classification of images with application to synthetic-aperture radar. Posterior probabilities are computed for candidate hypotheses using physical features estimated from sensor data along with features predicted from these hypotheses. The likelihood scoring allows propagation of uncertainty arising in both the sensor data and object models. The Bayesian classification, including the determination of a correspondence between unordered random features, is shown to be tractable, yielding a classification algorithm, a method for estimating error rates, and a tool for evaluating the performance sensitivity. The radar image features used for classification are point locations with an associated vector of physical attributes; the attributed features are adopted from a parametric model of high-frequency radar scattering. With the emergence of wideband sensor technology, these physical features expand interpretation of radar imagery to access the frequency- and aspect-dependent scattering information carried in the image phase.

Cell sectorization is used extensively to increase the capacity of cellular systems; however, inter-sector interference caused by non-ideal sector antennas hinders full realization of sectorization benefits. We propose a new technique for sector beam synthesis, using phased antenna arrays, to minimize inter-sector interference, or equivalently, to maximize the beam efficiency. A peak-to-peak ripple constraint on the power density inside the sector leads to a non-convex optimization task; a reparametrization results in an easily solved convex fractional linear program. The proposed procedure accommodates non-isotropic antenna elements, arbitrary element spacing, and arbitrary sector boundaries, but is limited to uniformly spaced linear (or planar) arrays. Finally, the proposed method is used to predict antenna array size requirements for a DS-CDMA cellular system.

In this paper, a method for estimating task execution times is presented in order to facilitate dynamic scheduling in a heterogeneous metacomputing environment. Execution time is treated as a random variable and is statistically estimated from past observations. This method predicts the execution time as a function of several parameters of the input data and does not require any direct information about the algorithms used by the tasks or the architecture of the machines. Techniques based upon the concept of analytic benchmarking/code profiling are used to characterize the performance differences between machines, allowing observations from dissimilar machines to be used when making a prediction. Experimental results are presented which use actual execution time data gathered from 16 heterogeneous machines.

High-frequency radar measurements of man-made targets are dominated by returns from isolated scattering centers, such as corners and flat plates. Characterizing the features of these scattering centers provides a parsimonious, physically relevant signal representation for use in automatic target recognition (ATR). In this paper, we present a framework for feature extraction predicated on parametric models for the radar returns. The models are motivated by the scattering behaviour predicted by the geometrical theory of diffraction. For each scattering center, statistically robust estimation of model parameters provides high-resolution attributes including location, geometry, and polarization response. We present statistical analysis of the scattering model to describe feature uncertainty, and we provide a least-squares algorithm for feature estimation. We survey existing algorithms for simplified models, and derive bounds for the error incurred in adopting the simplified models. A model order selection algorithm is given, and an M-ary generalized likelihood ratio test is given for classifying polarimetric responses in spherically invariant random clutter.

We present an adaptive compression and resampling technique using wavelet packet shrinkage. The motivating application is surface digitization for computer-aided manufacturing. The objective is to improve estimation accuracy using a sparse and irregular, but more accurate, resampling of the data. We provide modified thresholds for wavepacket shrinkage, heuristics for choosing the resampling grid, and a mean estimator using measured data. Computed results illustrate application of the proposed technique.

In most estimation and design problems, there exists more than one solution that satisfies all constraints. In this paper, we address the problem of estimating the complete set of feasible solutions. Multiple feasible solutions are frequently encountered in signal restoration, image reconstruction, array processing, system identification and filter design. An estimate of the size of the feasibility set can be utilized to quantitatively evaluate inclusion and effectiveness of added constraints. Further, set estimation can be used to determine a null feasibility set. We compute ellipsoidal approximations to the set of feasible solutions using a new ellipsoid algorithm and the method of analytic centers. Both algorithms admit multiple convex constraint sets with ease. Also, the algorithms provide a solution which is guaranteed to be in the interior of the feasibility set.

The distortion of a message due to channel noise can be alleviated significantly without redundant error control bits by judicious assignment of binary indices to message symbols. The nonredundant coding gain relies only on a notion of distance between symbols. In this paper, we consider the index assignment problem and adopt a minimax design criterion instead of the usual mean squared error (MSE) measure. The problem is found to be NP-hard, and an effective, heuristic, polynomial-time algorithm is presented for computing approximate solutions. The minimax criterion yields greatly improved worst case performance while maintaining good average performance. In addition, the familiar MSE criterion is shown likewise to yield an NP-hard index assignment task. The MSE problem is a special case of the classical quadratic assignment problem, for which computationally and theoretically useful results are available from the discrete mathematics literature.>

Biological compounds exhibit extraordinary functional specificity as a consequence of their precise spatial structure. Two signal recovery algorithms for computing molecular structure from noisy measurements of interatomic distances are presented. The problem is formulated as the minimization of a quadratic cost over the intersection of constraint sets. In a broader signal recovery context, a technique is utilized for iteratively computing the unique projection onto an intersection of closed convex sets, and the simplification possible with an appropriate choice of norm, despite a nonconvex constraint set, is illustrated.>

This paper presents a new algorithm for the extrapolation of multidimensional bandlimited sequences. The new algorithm is capable of incorporating prior knowledge of the concentration of signal energy on a finite region and imposes no restriction on either the location of observations from the multidimensional signal to be extrapolated or the shape of its passband.