There is growing interest in employing deep neural networks (DNN) for image sharpening. However, sharpening medical computed tomography (CT) images is challenging because sharpening substantially amplifies high-frequency noise. Alternatively, sharpening algorithms that are also designed to denoise produce images lacking texture. Most importantly, radiologists strongly prefer reading images at a consistent level of noise. Hence it is preferable that a sharpening algorithm not substantially change the noise energy or texture.In this work, we propose a noise preserving sharpening filter (NPSF) to sharpen CT images while keeping the noise energy and texture in the result similar to that of the input. We achieve this by adding appropriately scaled noise while training. Furthermore, the NPSF is characterized by three user-adjustable parameters which give flexibility to achieve a desired level of sharpness and noise. Our experiments show that the NPSF can sharpen noisy images while producing desired noise level and texture.

There is growing interest in the use of deep neural network (DNN) based image denoising to reduce patient’s X-ray dosage in medical computed tomography (CT). An effective denoiser must remove noise while maintaining the texture and detail. Commonly used mean squared error (MSE) loss functions in the DNN training weight errors due to bias and variance equally. However, the error due to bias is often more egregious since it results in loss of image texture and detail. In this paper, we present a novel approach to designing a loss function that penalizes variance and bias differently. Our proposed bias-reducing loss function allows us to train a DNN denoiser so that the amount of texture and detail retained can be controlled through a user adjustable parameter. Our experiments verify that the proposed loss function enhances the texture and detail in denoised images with only a slight increase in the MSE.

High-attenuation materials pose significant challenges to computed tomographic imaging. Formed of high mass-density and high atomic number elements, they cause more severe beam hardening and scattering artifacts than do water-like materials. Pre-corrected line-integral density measurements are no longer linearly proportional to the path lengths, leading to reconstructed image suffering from streaking artifacts extending from metal, often along highest-density directions. In this paper, a novel prior-based iterative approach is proposed to reduce metal artifacts. It combines the superiority of statistical methods with the benefits of sinogram completion methods to estimate and correct metal-induced biases. Preliminary results show minimized residual artifacts and significantly improved image quality.

Model-Based Iterative Reconstruction (MBIR) has shown promising results in clinical studies as they allow significant dose reduction during CT scans while maintaining the diagnostic image quality. MBIR improves the image quality over analytical reconstruction by modeling both the sensor (e.g., forward model) and the image being reconstructed (e.g., prior model). While the forward model is typically based on the physics of the sensor, accurate prior modeling remains a challenging problem. Markov Random Field (MRF) has been widely used as prior models in MBIR due to simple structure, but they cannot completely capture the subtle characteristics of complex images. To tackle this challenge, we generate a prior model by learning the desirable image property from a large dataset. Toward this, we use Plug-and-Play (PnP) framework which decouples the forward model and the prior model in the optimization procedure, replacing the prior model optimization by a image denoising operator. Then, we adopt the state-of-the-art deep residual learning for the image denoising operator which represents the prior model in MBIR. Experimental results on real CT scans demonstrate that our PnP MBIR with deep residual learning prior significantly reduces the noise and artifacts compared to analytical reconstruction and standard MBIR with MRF prior.

An increasing number of X-ray CT procedures are being conducted with drastically reduced dosage, due at least in part to advances in statistical reconstruction methods that can deal more effectively with noise than can traditional techniques. As data become photon-limited, more detailed models are necessary to deal with count rates that drop to the levels of system electronic noise. We present two options for sinogram pre-treatment that can improve the performance of photon-starved measurements, with the intent of following with model-based image reconstruction. Both the local linear minimum mean-squared error (LLMMSE) filter and pointwise Bayesian restoration (PBR) show promise in extracting useful, quantitative information from very low-count data by reducing local bias while maintaining the lower noise variance of statistical methods. Results from clinical data demonstrate the potential of both techniques.

X-ray detectors in clinical computed tomography (CT) usually operate in current-integrating mode. Their complicated signal statistics often lead to intractable likelihood functions for practical use in model-based image reconstruction (MBIR). It is therefore desirable to design simplified statistical models without losing the essential factors. Depending on whether the CT transmission data are logarithmically transformed, pre-log and post-log models are two major categories of choices in CT MBIR. Both being approximations, it remains an open question whether one model can notably improve image quality over the other on real scanners. In this study, we develop and compare several pre-log and post-log MBIR algorithms under a unified framework. Their reconstruction accuracy based on simulation and clinical datasets are evaluated. The results show that pre-log MBIR can achieve notably better quantitative accuracy than post-log MBIR in ultra-low-dose CT, although in less extreme cases, post-log MBIR with handcrafted pre-processing remains a competitive alternative. Pre-log MBIR could play a growing role in emerging ultra-low-dose CT applications.

Dual-energy X-ray CT (DECT) has the potential to improve contrast and reduce artifacts as compared to traditional CT. Moreover, by applying model-based iterative reconstruction (MBIR) to dual-energy data, one might also expect to reduce noise and improve resolution. However, the direct implementation of dual-energy MBIR requires the use of a nonlinear forward model, which increases both complexity and computation. Alternatively, simplified forward models have been used which treat the material-decomposed channels separately, but these approaches do not fully account for the statistical dependencies in the channels. In this paper, we present a method for joint dual-energy MBIR (JDE-MBIR), which simplifies the forward model while still accounting for the complete statistical dependency in the material-decomposed sinogram components. The JDE-MBIR approach works by using a quadratic approximation to the polychromatic log-likelihood and a simple but exact nonnegativity constraint in the image domain. We demonstrate that our method is particularly effective when the DECT system uses fast kVp switching, since in this case the model accounts for the inaccuracy of interpolated sinogram entries. Both phantom and clinical results show that the proposed model produces images that compare favorably in quality to previous decomposition-based methods, including FBP and other statistical iterative approaches.

Recent applications of model-based iterative reconstruction (MBIR) algorithms to multislice helical CT reconstructions have shown that MBIR can greatly improve image quality by increasing resolution as well as reducing noise and some artifacts. However, high computational cost and long reconstruction times remain as a barrier to the use of MBIR in practical applications. Among the various iterative methods that have been studied for MBIR, iterative coordinate descent (ICD) has been found to have relatively low overall computational requirements due to its fast convergence. This paper presents a fast model-based iterative reconstruction algorithm using spatially nonhomogeneous ICD (NH-ICD) optimization. The NH-ICD algorithm speeds up convergence by focusing computation where it is most needed. The NH-ICD algorithm has a mechanism that adaptively selects voxels for update. First, a voxel selection criterion VSC determines the voxels in greatest need of update. Then a voxel selection algorithm VSA selects the order of successive voxel updates based upon the need for repeated updates of some locations, while retaining characteristics for global convergence. In order to speed up each voxel update, we also propose a fast 1-D optimization algorithm that uses a quadratic substitute function to upper bound the local 1-D objective function, so that a closed form solution can be obtained rather than using a computationally expensive line search algorithm. We examine the performance of the proposed algorithm using several clinical data sets of various anatomy. The experimental results show that the proposed method accelerates the reconstructions by roughly a factor of three on average for typical 3-D multislice geometries.

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

We quantitatively compare filtered backprojection (FBP), expectation-maximization (EM), and Bayesian reconstruction algorithms as applied to the IndyPET scanner--a dedicated research scanner which has been developed for small and intermediate field of view imaging applications. In contrast to previous approaches that rely on Monte Carlo simulations, a key feature of our investigation is the use of an empirical system kernel determined from scans of line source phantoms. This kernel is incorporated into the forward model of the EM and Bayesian algorithms to achieve resolution recovery. Three data sets are used, data collected on the IndyPET scanner using a bar phantom and a Hoffman three-dimensional brain phantom, and simulated data containing a hot lesion added to a uniform background. Reconstruction quality is analyzed quantitatively in terms of bias-variance measures (bar phantom) and mean square error (lesion phantom). We observe that without use of the empirical system kernel, the FBP, EM, and Bayesian algorithms give similar performance. However, with the inclusion of the empirical kernel, the iterative algorithms provide superior reconstructions compared with FBP, both in terms of visual quality and quantitative measures. Furthermore, Bayesian methods outperform EM. We conclude that significant improvements in reconstruction quality can be realized by combining accurate models of the system response with Bayesian reconstruction algorithms.

We introduce an adaptive wavelet graph image model applicable to Bayesian tomographic reconstruction and other problems with nonlocal observations. The proposed model captures coarse-to-fine scale dependencies in the wavelet tree by modeling the conditional distribution of wavelet coefficients given overlapping windows of scaling coefficients containing coarse scale information. This results in a graph dependency structure which is more general than a quadtree, enabling the model to produce smooth estimates even for simple wavelet bases such as the Haar basis. The inter-scale dependencies of the wavelet graph model are specified using a spatially nonhomogeneous Gaussian distribution with parameters at each scale and location. The parameters of this distribution are selected adaptively using nonlinear classification of coarse scale data. The nonlinear adaptation mechanism is based on a set of training images. In conjunction with the wavelet graph model, we present a computationally efficient multiresolution image reconstruction algorithm. This algorithm is based on iterative Bayesian space domain optimization using scale recursive updates of the wavelet graph prior model. In contrast to performing the optimization over the wavelet coefficients, the space domain formulation facilitates enforcement of pixel positivity constraints. Results indicate that the proposed framework can improve reconstruction quality over fixed resolution Bayesian methods.

We introduce a spatially non-homogeneous adaptive image model and multiresolution reconstruction algorithm for Bayesian tomographic reconstruction. In contrast to existing approaches, the proposed image model is formulated in a multiresolution wavelet domain and relies on training data to incorporate the expected characteristics of typical reconstructions. The actual tomographic reconstruction is performed in the space domain to simplify enforcement of the positivity constraint. We apply the proposed algorithm to simulated data and to data acquired using the IndyPET dedicated research scanner. Our experimental results indicate that our algorithm can improve reconstruction quality over fixed resolution Bayesian methods.

Bayesian tomographic reconstruction algorithms generally require the efficient optimization of a functional of many variables. In this setting, as well as in many other optimization tasks, functional substitution (FS) has been widely applied to simplify each step of the iterative process. The function to be minimized is replaced locally by an approximation having a more easily manipulated form, e.g., quadratic, but which maintains sufficient similarity to descend the true functional while computing only the substitute. We provide two new applications of FS methods in iterative coordinate descent for Bayesian tomography. The first is a modification of our coordinate descent algorithm with one-dimensional (1-D) Newton-Raphson approximations to an alternative quadratic which allows convergence to be proven easily. In simulations, we find essentially no difference in convergence speed between the two techniques. We also present a new algorithm which exploits the FS method to allow parallel updates of arbitrary sets of pixels using computations similar to iterative coordinate descent. The theoretical potential speed up of parallel implementations is nearly linear with the number of processors if communication costs are neglected.

In this research, rather than developing a forward model to be inverted, we propose directly modeling the inverse operator. The goal is to develop a non-iterative Bayesian reconstruction method which requires computation comparable to conventional FBP methods, but achieves quality competitive with that of iterative Bayesian methods such as maximum a posteriori probability (MAP). The method we propose, which we call nonlinear back projection (NBP), forms a back projected image cross-section by applying nonlinear filters to the projected data. This method attempts to directly model a type of optimal inverse operator through off-line training of the non-linear filters using example training data of known image cross sections and noisy realizations of projections. The Radon domain filtering is two-dimensional, exploiting redundancy among adjacent angles' measurements. This direct approach to modeling the inverse operator has several potential advantages which make it interesting. First, the elimination of iterative estimation should save computation time relative to common Bayesian techniques. Secondly, some of the inherently nonlinear attributes of the forward process may be implicitly incorporated into the training of the nonlinear backprojection. Finally, training based on sample images and projections may more effectively incorporate greater complexity in the statistical behavior of images than the simple Markov random field models found in most Bayesian formulations.

Markov random fields (MRF's) have been widely used to model images in Bayesian frameworks for image reconstruction and restoration. Typically, these MRF models have parameters that allow the prior model to be adjusted for best performance. However, optimal estimation of these parameters(sometimes referred to as hyper parameters) is difficult in practice for two reasons: i) direct parameter estimation for MRF's is known to be mathematically and numerically challenging; ii)parameters can not be directly estimated because the true image cross section is unavailable.In this paper, we propose a computationally efficient scheme to address both these difficulties for a general class of MRF models,and we derive specific methods of parameter estimation for the MRF model known as generalized Gaussian MRF (GGMRF).The first section of the paper derives methods of direct estimation of scale and shape parameters for a general continuously valued MRF. For the GGMRF case, we show that the ML estimate of the scale parameter, sigma, has a simple closed-form solution, and we present an efficient scheme for computing the ML estimate of the shape parameter, p, by an off-line numerical computation of the dependence of the partition function on p.The second section of the paper presents a fast algorithm for computing ML parameter estimates when the true image is unavailable. To do this, we use the expectation maximization(EM) algorithm. We develop a fast simulation method to replace the E-step, and a method to improve parameter estimates when the simulations are terminated prior to convergence.Experimental results indicate that our fast algorithms substantially reduce computation and result in good scale estimates for real tomographic data sets.

In many applications such as nondestructive testing (NDT), we search for an anomaly (air hole, inclusion) inside a homogeneous region (metal). This problem classically is done in three steps: detection, localization and characterization. The present industrial techniques do well in the two first steps, but the exact determination of the shape of the default region is still in the research domain. The computational cost of the classical tomographic reconstruction using the pixel (2D) or the voxel (3D) representation of the examined body still hinders its use in industrial applications. We propose modelling the contour (or the surface) of the default region by a polygon (or by a polyhedron) and estimating directly the coordinates of its vertices from very limited tomographic projection data.

A certain class of Markov random fields (MRF) known as generalized Gaussian MRFs (GGMRF) have been shown to yield good performance in modeling the a priori information in Bayesian image reconstruction and restoration problems. Though the ML estimate of temperature T of a GGMRF has a closed form solution, the optimal estimation of the shape parameter p is a difficult problem due to the intractable nature of the partition function. We present a tractable scheme for ML estimation of p by an off-line numerical computation of the log of the partition function. In image reconstruction or restoration problems, the image itself is not known. To address this problem, we use the EM algorithm to compute the estimates directly from the data. For efficient computation of the expectation step, we propose a fast simulation technique and a method to extrapolate the estimates when the simulations are terminated prematurely prior to convergence. Experimental results show that the proposed methods result in substantial savings in computation and superior quality images.

The popularity of Bayesian methods in image processing applications has generated great interest in image modeling. A good image model needs to be non-homogeneous to be able to adapt to the local characteristics of the different regions in an image. In the past however, such a formulation was difficult since it was not clear as to how to choose the parameters of the non-homogeneous model. But now motivated by results in maximum likelihood parameter estimation of MRF models, we formulate in this paper a non-homogeneous Markov random field (MRF) image model in the multiresolution framework. The advantage of the multiresolution framework is two fold: first, it makes it possible to estimate the parameters of the nonhomogeneous MRF at any resolution by using the image at the coarser resolution. Second, it yields multiresolution algorithms which are computationally efficient and more robust than their single resolution counterparts. Experimental results in tomographic image reconstruction and optical flow computation problems verify the superior modeling provided by the new model.

Statistical tomographic reconstruction algorithms generally require the efficient optimization of a functional. An algorithm known as iterative coordinate descent with Newton-Raphson updates (ICD/NR) has been shown to be much more computationally efficient than indirect optimization approaches based on the EM algorithm. However, while the ICD/NR algorithm has experimentally been shown to converge stably, no theoretical proof of convergence is known. We prove that a modified algorithm, which we call ICD functional substitution (ICD/FS), has guaranteed global convergence in addition to the computational efficiency of the ICD/NR. The ICD/FS method works by approximating the log likelihood at each pixel by an alternative quadratic functional. Experimental results show that the convergence speed of the globally convergent algorithm is nearly identical to that of ICD/NR.

Several efficient techniques have previously been proposed to reduce the computational burden of block matching for motion estimation in video coding. The goal is efficient motion estimation with minimal error in the motion-compensated predicted image. We present a block motion estimation scheme which is based on matching of integral projections of motion blocks with those of the search area in the previous frame. Like many other techniques, ours operates in a sequence of decreasing search radii, but it performs an exhaustive search at each level of the hierarchy. The projection method is much less computationally costly than block matching and has a prediction accuracy of competitive quality with both full block matching and other efficient techniques. Our algorithm also takes advantage of the similarity of motion vectors in adjacent blocks in typical imagery by subsampling the motion vector field. It has the added advantage of allowing parallel computation of vertical and horizontal displacements.

Over the past years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms take an indirect approach based on the expectation maximization (EM) algorithm. We propose a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion. The key to this direct optimization approach is greedy pixel-wise computations known as iterative coordinate decent (ICD). We propose a novel method for computing the ICD updates, which we call ICD/Newton-Raphson. We show that ICD/Newton-Raphson requires approximately the same amount of computation per iteration as EM-based approaches, but the new method converges much more rapidly (in our experiments, typically five to ten iterations). Other advantages of the ICD/Newton-Raphson method are that it is easily applied to MAP estimation of transmission tomograms, and typical convex constraints, such as positivity, are easily incorporated.

Bayesian methods have proven to be powerful tools for computed tomographic reconstruction in realistic physical problems. However, Bayesian methods require that a number of modeling and computational problems be addressed. The paper summarizes a coherent system of statistical modeling and optimization techniques designed to facilitate efficient, unsupervised Bayesian emission and transmission tomographic reconstruction. New results are included on improved convergence behavior of these methods.

X-ray and /spl gamma/-ray radiography have been indispensable techniques for materials inspection for many years. Internal structure is typically inferred from radiographs by human evaluation. More precise information is possible if the function of three spatial variables can be estimated directly from the radiographic data. Several mathematical inversion formulae have been derived for deterministic reconstruction from the cone-beam integral projection data represented by the radiographs, but depend on large numbers of measurements for usable reconstructions. Bayesian statistical approaches are more robust to data limitations, and can function usefully in the presence of severe system limitations. The solution of the estimation problem, however, is an formidable numerical challenge, requiring inordinate amounts of computing power and data storage for quality reconstructions. This paper presents techniques for reducing the computation time and storage requirements for iterative approximation from digitized radiographs. Examples of these reconstructions are provided for physical experiments with steel samples imaged on radiographic film.

While Bayesian methods can significantly improve the quality of tomographic reconstructions, they require the solution of large iterative optimization problems. Recent results indicate that the convergence of these optimization problems can be improved by using sequential pixel updates, or Gauss-Seidel iterations. However, Gauss-Seidel iterations may be perceived as less useful when parallel computing architectures are use. We show that for degrees of parallelism of typical practical interest, the Gauss-Seidel iterations updates may be computed in parallel with little loss in convergence speed. In this case, the theoretical speed up of parallel implementations is nearly linear with the number of processors.

This paper presents the exact maximum likelihood (ML) estimate of temperature for a class of Markov random fields (MRF) known as generalized Gaussian MRFs. The ML estimate has a simple closed form which is analogous to variance estimation for Gaussian random variables. This result is useful because the temperature parameter plays the important role of determining the amount of smoothing in problems such as Bayesian image reconstruction and restoration. Two extensions of the basic result are also given: 1) numerical scale estimation for the general class of continuous MRFs; and 2) parameter estimation from incomplete data using the EM algorithm. Preliminary numerical experiments support the usefulness of the technique.>

The Hough transform is a relatively simple and robust method for detection of economically parameterized geometric features via accumulators in the discretized parameter space. Several methods for detecting circular structure have been proposed, with centers of circles often detected as intersections of normals to the tangents of curves. We modify the transform to detect general rotationally invariant, continuously-valued image features, based on gradient measurements independent of radii. This method is robust to uncertainties in surfaces which are poorly modeled by standard stochastic models. Examples of application of the transform are from paleontological classification of digitized fossil molar surfaces.>

Bayesian reconstruction and restoration methods require the choice of parameters related to variance in both stochastic image models and observed data. In practice these parameters, or their ratio, is often chosen heuristically. The authors present a method for joint maximum-likelihood (ML) estimation of these two parameters in transmission tomography, with emphasis on the X-ray//spl gamma/-ray dosage parameter. The estimation algorithm employs the expectation-maximization method, with the unobserved image as the complete data. The ML parameter estimator is shown to yield values which are practical for tomographic reconstruction, both with synthetic phantoms and real data.>

Block-based motion estimation is included in most video coding systems, despite the high computational cost of direct block matching techniques. Several schemes have been advanced in recent years to simplify motion estimation while maintaining minimal error in the motion- compensated predicted image. We present in this paper a block motion estimation approach which is based on exhaustive search with integral projections. The projection method is much less computationally costly than block matching, and has a prediction accuracy of competitive quality with both full block matching and other efficient techniques. Our algorithm also takes advantage of the similarity of motion vectors in adjacent blocks in typical imagery, by subsampling the motion vector field.

The authors present a Markov random field model which allows realistic edge modeling while providing stable maximum a posterior (MAP) solutions. The model, referred to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisfies several desirable analytical and computational properties for map estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the a posteriori log-likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low-dosage transmission tomography.

A method is presented for Bayesian reconstruction from projections which updates single pixel values, rather than the entire image, at each step. The technique is similar to Gauss-Seidel (GS) iteration for the solution of differential equations on finite grids. The computational cost per iteration of the GS approach is found to be approximately equal to that of gradient methods. For continuously valued images, GS is found to have significantly better convergence at modes representing high spatial frequencies. In addition, GS is well-suited to segmentation when the image is constrained to be discrete-valued.>

Low bit-rate image coding results in artifacts at reconstruction whose characteristics depend on the form of the coding/decoding algorithm used. A very common and visually objectionable effect of most coding methods is distortion of edges. Classical spatially-invariant filtering techniques are of little use in removing this signal-dependent reconstruction error. We present an algorithm for enhancement of edge quality through nonstationary filtering based on estimates of edge locations. Edge detection and enhancement are performed by a sequence of simple one-dimensional processes. The algorithm yields appreciable improvement when applied to images coded by pixel-domain methods.

An algorithm which approximates the maximum likelihood estimator (MLE) for the locations of constant-density discs in integral projection data is presented. The algorithm is of linear complexity in the object count and requires only approximately 25% more computation than the MLE of the single-location problem. Approximation error analysis, in terms of error probability, is provided through empirical matching of densities for the extremal values of the random-noise field.>

The authors discuss a way to improve transmission tomograms in the presence of large density data variations and low photon dosage. They present a design for nonstationary filters that exploits the detectability of high-density regions in the object to match filters to local noise properties. The design of each filter is formulated as a least-squares optimization problem, with linear equality and inequality constraints that protect the resolution of detail while minimizing noise power in the reconstruction. Experimental results show reconstructions in whitened noise of power equivalent to those of conventional convolution backprojection, but with significantly better resolution.>

A number of different methods for reconstruction of bandlimited 1-D and 2-D signals from nonuniformly spaced samples are compared experimentally. The six 1-D algorithms are solution for Fourier series coefficients, two methods due to Yen, Papoulis' coordinate transformation, cubic splines, and an iterative method similar to those of Wiley and Gerchberg. Three of the 2-D algorithms are iterative. They differ in the mode of space domain error correction. The fourth 2-D algorithm is the thin-plate splines method. The methods are evaluated on the basis of mean signal-to-error energy ratios calculated over an ensemble consisting of reconstructions of several functions, each sampled with many different random point sets. Sample plots of reconstructions are also included.