Model based iterative reconstruction (MBIR) algorithms have shown significant improvement in CT image
quality by increasing resolution as well as reducing noise and artifacts. In diagnostic protocols, radiologists
often need the high-resolution reconstruction of a limited region of interest (ROI). This ROI reconstruction
is complicated for MBIR which should reconstruct an image in a full field of view (FOV) given full sinogram
measurements. Multi-resolution approaches are widely used for this ROI reconstruction of MBIR, in which the
image with a full FOV is reconstructed in a low-resolution and the forward projection of non-ROI is subtracted
from the original sinogram measurements for high-resolution ROI reconstruction. However, a low-resolution
reconstruction of a full FOV can be susceptible to streaking and blurring artifacts and these can be propagated
into the following high-resolution ROI reconstruction. To tackle this challenge, we use a coupled dictionary
representation model between low- and high-resolution training dataset for artifact removal and super resolution
of a low-resolution full FOV reconstruction. Experimental results on phantom data show that the restored full
FOV reconstruction via a coupled dictionary learning significantly improve the image quality of high-resolution
ROI reconstruction for MBIR.
Dose reduction in clinical X-ray computed tomography (CT) causes low signal-to-noise ratio (SNR) in photonsparse situations. Statistical iterative reconstruction algorithms have the advantage of retaining image quality while reducing input dosage, but they meet their limits of practicality when significant portions of the sinogram near photon starvation. The corruption of electronic noise leads to measured photon counts taking on negative values, posing a problem for the log() operation in preprocessing of data. In this paper, we propose two categories of projection correction methods: an adaptive denoising filter and Bayesian inference. The denoising filter is easy to implement and preserves local statistics, but it introduces correlation between channels and may affect image resolution. Bayesian inference is a point-wise estimation based on measurements and prior information. Both approaches help improve diagnostic image quality at dramatically reduced dosage.
Model- based iterative reconstruction (MBIR) is increasingly widely applied as an improvement over conventional, deterministic methods of image reconstruction in X-ray CT. A primary advantage of MBIR is potentially dras tically reduced dosage without diagnostic quality loss. Early success of the method has naturally led to growing numbers of scans at very low dose, presenting data which does not match well the simple statistical models heretofore considered adequate. This paper addresses several issues arising in limiting cases which call for refine ment of standard data models. The emergence of electronic noise as a significant contributor to uncertainty, and bias of sinogram values in photon-starved measurements are demonstrated to be important modeling problems in this new environment. We present also possible ameliorations to several of these low-dosage estimation issues.
Bayesian estimation is a statistical approach for incorporating prior information through the choice of an a
priori distribution for a random field. A priori image models in Bayesian image estimation are typically low-order
Markov random fields (MRFs), effectively penalizing only differences among immediately neighboring
voxels. This limits spectral description to a crude low-pass model. For applications where more flexibility in
spectral response is desired, potential benefit exists in models which accord higher a priori probability to content
in higher frequencies. Our research explores the potential of larger neighborhoods in MRFs to raise the number
of degrees of freedom in spectral description. Similarly to classical filter design, the MRF coefficients may be
chosen to yield a desired pass-band/stop-band characteristic shape in the a priori model of the images. In this
paper, we present an alternative design method, where high-quality sample images are used to estimate the MRF
coefficients by fitting them into the spatial correlation of the given ensemble. This method allows us to choose
weights that increase the probability of occurrence of strong components at particular spatial frequencies. This
allows direct adaptation of the MRFs for different tissue types based on sample images with different frequency
content. In this paper, we consider particularly the preservation of detail in bone structure in X-ray CT. Our
results show that MRF design can be used to obtain bone emphasis similar to that of conventional filtered
back-projection (FBP) with a bone kernel.
We introduce a post-processing approach to improve the quality of CT reconstructed images. The scheme is
adapted from the resolution-synthesis (RS)1 interpolation algorithm. In this approach, we consider the input
image, scanned at a particular dose level, as a degraded version of a high quality image scanned at a high
dose level. Image enhancement is achieved by predicting the high quality image by classification based linear
regression. To improve the robustness of our scheme, we also apply the minimum description length principle
to determine the optimal number of predictors to use in the scheme, and the ridge regression to regularize the
design of the predictors. Experimental results show that our scheme is effective in reducing the noise in images
reconstructed from filtered back projection without significant loss of image details. Alternatively, our scheme
can also be applied to reduce dose while maintaining image quality at an acceptable level.
Model based iterative reconstruction (MBIR) algorithms have recently been applied to computed tomography and
demonstrated superior image quality. This algorithmic framework also provides us the flexibility to incorporate
more sophisticated models of the data acquisition process. In this paper, we present the kinetic parameter
iterative reconstruction (KPIR) algorithm which estimates voxel values as a function of time in the MBIR
framework. We introduce a parametric kinetic model for each voxel, and estimate the kinetic parameters directly
from the data. Results on phantom study and clinical data show that the proposed method can significantly
reduce motion artifacts in the reconstruction.
Medical imaging typically requires the reconstruction of a limited region of interest (ROI) to obtain a high
resolution image of the anatomy of interest. Although targeted reconstruction is straightforward for analytical
reconstruction methods, it is more complicated for statistical iterative techniques, which must reconstruct all
objects in the field of view (FOV) to account for all sources of attenuation along the ray paths from x-ray
source to detector. A brute force approach would require the reconstruction of the full field of view in high-resolution,
but with prohibitive computational cost. In this paper, we propose a multi-resolution approach to
accelerate targeted iterative reconstruction using the non-homogeneous ICD (NH-ICD) algorithm. NH-ICD aims
at speeding up convergence of the coordinate descent algorithm by selecting preferentially those voxels most in
need of updating. To further optimize ROI reconstruction, we use a multi-resolution approach which combines
three separate improvements. First, we introduce the modified weighted NH-ICD algorithm, which weights the
pixel selection criteria according to the position of the voxel relative to the ROI to speed up convergence within
the ROI. Second, we propose a simple correction to the error sinogram to correct for inconsistencies between
resolutions when the forward model is not scale invariant. Finally, we leverage the flexibility of the ICD algorithm
to add selected edge pixels outside the ROI to the ROI reconstruction in order to minimize transition artifacts
at the ROI boundary. Experiments on clinical data illustrate how each component of the method improves
convergence speed and image quality.
Statistical reconstruction methods show great promise for improving resolution, and reducing noise and artifacts
in helical X-ray CT. In fact, statistical reconstruction seems to be particularly valuable in maintaining reconstructed
image quality when the dosage is low and the noise is therefore high. However, high computational
cost and long reconstruction times remain as a barrier to the use of statistical reconstruction in practical applications.
Among the various iterative methods that have been studied for statistical reconstruction, iterative
coordinate descent (ICD) has been found to have relatively low overall computational requirements due to its
This paper presents a novel method for further speeding the convergence of the ICD algorithm, and therefore
reducing the overall reconstruction time for statistical reconstruction. The method, which we call nonhomogeneous
iterative coordinate descent (NH-ICD) uses spatially non-homogeneous updates to speed convergence
by focusing computation where it is most needed. Experimental results with real data indicate that the
method speeds reconstruction by roughly a factor of two for typical 3D multi-slice geometries.
Computed Tomography (CT) screening and pediatric imaging, among other applications, demand the development of more efficient reconstruction techniques to diminish radiation dose to the patient. While many methods are proposed to limit or modulate patient exposure to x-ray at scan time, the resulting data is excessively noisy, and generates image artifacts unless properly corrected. Statistical iterative reconstruction (IR) techniques have recently been introduced for reconstruction of low-dose CT data, and rely on the accurate modeling of the distribution of noise in the acquired data. After conversion from detector counts to attenuation measurements, however, noisy data usually deviate from simple Gaussian or Poisson representation, which limits the ability of IR to generate artifact-free images. This paper introduces a recursive filter for IR, which conserves the statistical
properties of the measured data while pre-processing attenuation measurements. A basic framework for inclusion of detector electronic noise into the statistical model for IR is also presented. The results are shown to successfully eliminate streaking artifacts in photon-starved situations.
Recently, there has been interest in estimating kinetic model parameters for each voxel in a PET image. To do this, 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 EM algorithm for direct parametric reconstruction. More recently, researchers have developed semi-direct methods which use spline-based reconstruction, or direct methods for estimation of kinetic parameters from image regions. However, direct voxel-wise parametric reconstruction has remained a challenge due to the unsolved complexities of inversion and required spatial regularization. In this work, we demonstrate an efficient method for direct voxel-wise reconstruction of kinetic parameters (as a parametric image) from 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. This PICD algorithm is computationally efficient and allows the physiologically important kinetic parameters to be spatially regularized. Our experimental simulations demonstrate that direct parametric reconstruction can substantially reduce estimation error of kinetic parameters as compared to indirect methods.
It is often necessary to analyze the time response of a tracer. A common way of analyzing the tracer time response is to use a compartment model and estimate the model parameters. The model parameters are generally physiologically meaningful and called "kinetic parameters". In this paper, we simultaneously estimate both the kinetic parameters at each voxel and the model-based plasma input function directly from the sinogram data. Although the plasma model parameters are not our primary interest, they are required for accurate reconstruction of kinetic parameters. The plasma model parameters are initialized with an image domain method to avoid local minima, and multiresolution optimization is used to perform the required reconstruction. Good initial guesses for the plasma parameters are required for the algorithm to converge to the correct answer. Therefore, we devised a preprocessing step involving clustering of the emission images by temporal characteristics to find a reasonable plasma curve that was consistent with the kinetics of the multiple tissue types. We compare the root mean squared error (RMSE) of the kinetic parameter estimates with the measured (true) plasma input function and with the estimated plasma input function.
Tests using a realistic rat head phantom and a real plasma input function show that we can simultaneously estimate the kinetic parameters of the two-tissue compartment model and plasma input function. The RMSE of the kinetic parameters increased for some parameters and remained the same or decreased for other parameters.
Magnetic resonance imaging (MRI) is used, in addition to its well known medical and biological applications, for the study of a variety of fluid dynamic phenomena. This paper focuses on the MRI imaging
of liquid foams to aid the study of their temporal and spatial dynamics. The three dimensional image reconstruction problem is relatively low SNR, with the ultimate goal of analyzing the foam's structure and its evolution. We demonstrate substantial improvement of image quality with Bayesian estimation using simple edge preserving
Markov random field (MRF) models of the fluid field. In terms of total computation time, speed of convergence of estimates is similar
between gradient based methods and sequential greedy voxel updates, with the former requiring more iterations and the latter requiring more operations per iteration. The paper shows also some preliminary results in the analysis of the reconstructed imagery using a
simple parametric model of foam cells.
In this paper we introduce a Bayesian tomographic reconstruction technique employing a wavelet-based multiresolution prior model. While the image is modeled in the wavelet-domain, the actual tomographic reconstruction is performed in a fixed resolution pixel domain. In comparison to performing the reconstruction in the wavelet domain, the pixel based optimization facilitates enforcement of the positivity constraint and preserves the sparseness of the tomographic projection matrix. Thus our technique combines the advantages of multiresolution image modeling with those of performing the constrained optimization in the pixel domain. In addition to this reconstruction framework, we introduce a novel multiresolution prior model. This prior model attempts to capture the dependencies of wavelet coefficients across scales by using a Markov chain structure. Specifically, the model employs nonlinear predictors to locally estimate the prior distribution of wavelet coefficients from coarse scale information. We incorporate this prior into a coarse-to-fine scale tomographic reconstruction algorithm. Preliminary results indicate that this algorithm can potentially improve reconstruction quality over fix resolution Bayesian methods.
Emission Computed Tomography (ECT) is widely applied in medical diagnostic imaging, especially to determine physiological function. The available set of measurements is,however, often incomplete and corrupted, and the quality of image reconstruction is enhanced by the computation of a statistically optimal estimate. We present here a numerical method of ECT image reconstruction based on a Taylor series quadratic approximation to the usual Poison log-likelihood function. The quadratic approximation yields simplification in understanding and manipulating Poisson models. We introduce an algorithm similar to global Newton methods which updates the point of expansion a limited number of time sand we give quantitative measures of the accuracy of the reconstruction. The result show little difference in quality from those obtained with the exact Poisson model.
NonGaussian Markov image models are effective in the preservation of edge detail in Bayesian formulations of restoration and reconstruction problems. Included in these models are coefficients quantifying the statistical links among pixels in local cliques, which are typically assumed to have an inverse dependence on distance among the corresponding neighboring pixels. Estimation of these coefficients is a nontrivial task for Non Gaussian models. We present rules for coefficient estimation for edge- preserving models which are particularly effective for edge preservation and noise suppression, using a predictive technique analogous to estimation of the weights of optimal weighted median filters.
The computational burden of full search block matching algorithms for motion estimation in video coding can be reduced through exploitation of spatial and temporal correlation of the motion vectors. This paper describes a simple adaptive temporal prediction scheme for block motion vectors. The first-order temporal predictor determines the center of the search area for a conventional block match, but with substantially reduced search radius. The abbreviated search reduces computation by about 75% for blocks whose motion is successfully predicted. Adaptivity is introduced through the notion of ambiguity in the predicted block match. Those blocks whose matching cost function shows too great an ambiguity in the neighborhood of the best match are instead estimated by the conventional full search. While performance of the algorithm is dependent on sequence content, it offers an attractive choice in the computational cost/performance tradeoff for simple motion compensation.
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.
Bayesian estimation of transmission tomographic images presents formidable optimization tasks. Numerical solutions of this problem are limited in speed of convergence by the number of iterations required for the propagation of information across the grid. Edge-preserving prior models for tomographic images inject a nonlinear element into the Bayesian cost function, which limits the effectiveness of algorithms such as conjugate gradient, intended for linear problems. In this paper, we apply nonlinear multigrid optimization to Bayesian reconstruction of a two-dimensional function from integral projections. At each resolution, we apply Gauss-Seidel type iterations, which optimize locally with respect to individual pixel values. If the cost function is differentiable, the algorithm speeds convergence; if it is nonconvex and/or nondifferentiable, multigrid can yield improved estimates.
We present a sub-band image coding/decoding system using a diamond-shaped pyramid frequency decomposition to more closely match visual sensitivities than conventional rectangular bands. Filter banks are composed of simple, low order IIR components. The coder is especially designed to function in a multiple resolution reconstruction setting, in situations such as variable capacity channels or receivers, where images must be reconstructed without the entire pyramid of sub-bands. We use a nonlinear interpolation technique for lost subbands to compensate for loss of aliasing cancellation.
We present an algorithm for Bayesian estimation of temporally active spatial regions of video sequences. The algorithm improves the effectiveness of conditional replenishment for video compression in many applications which feature a background/foreground format. For the sake of compatibility with prevalent block-type coders, the binaryvalued segmentation is constrained to be constant on square blocks of 8x8 or 16 x 16 pixels. Our approach favors connectivity at two levels of scale. The first is at the individual pixel level, where a Gibbs distribution is used for the active pixels in the binary field of supra-threshold interframe differences. The final segmentation also assigns higher probability to patterns of active blocks which are connected, since in general, macroscopic entities are assumed to be many blocks in size. Demonstrations of the advantage of the Bayesian approach are given through simulations with standard sequences.