Computerized evaluation of image reconstruction algorithms

Abstract

In medical imaging an enormous variety of algorithms have been proposed to reconstruct a cross section of the human body. In assessing the relative task‐oriented performance of reconstruction algorithms, it is desirable to assign statistical significance to claims of superiority of one algorithm over another. However, very often the achievement of statistical significance demands a large number of observations. Performing such an evaluation on mathematical phantoms requires a means of running the competing algorithms on projection data obtained from a large number of randomly generated phantoms. Thereafter, various numerical measures of agreement between the reconstructed images and the original phantoms may be used to reach a conclusion which has some statistical substance. In this article we describe the software SuperSNARK, which automates an evaluation methodology for assigning statistical significance to the observed differences in performance of two or more image reconstruction algorithms. As a demonstration, we compare the relative efficacy of the maximum likelihood expectation maximization (ML‐EM) algorithm and the filtered backprojection (FBP) method for performing three medical tasks in positron emission tomography (PET)—estimation of total uptake by structures, detection of relatively higher uptake between pairs of symmetric structures, and estimation of uptake at individual points within structures. We find that for estimating total uptake ML‐EM outperforms FBP, for detecting relatively higher uptake there is not a statistically significant difference between the two methods, and for estimating pointwise uptake FBP outperforms ML‐EM. It is demonstrated that SuperSNARK makes it easy to apply the methodology of statistical hypothesis testing to substantiate such claims of task‐specific superiority of one reconstruction algorithm over another. © 1996 John Wiley & Sons, Inc.

Bayesian image reconstruction using image-modeling Gibbs priors

“…the reconstructed values; the a i 's and b i 's are algorithm-specific coefficients to be determined from training data. We have included the higher-order terms in Equation (15) to allow for possi-We estimated the noise models for FBP with the free parameters ble algorithm-dependent nonlinearity, although we expect the of the algorithms chosen based on some medically relevant figfirst-order terms to be the dominant components in many situaure of merit [ 25 ] . ( The free parameter is the filter cutoff f r .)…”

“…For the restoration in the second stage, we employed It is worth pointing out, however, that the noise model itself depends on the signal-to-noise ratio of the measurement process an approximate version of the Gibbs Sampler referred to as the 5-union algorithm in [30]. With this approximation, instead of (in our case, the coincidence count [25]), but this can usually be predetermined in practice. Furthermore, the noise at a pixel taking a sample from the local conditional distribution supported on [0, 255] at each step, we take one from the local conditional may depend on the values of pixels beyond its eight nearest neighbors, and one may need a more sophisticated model de-distribution truncated to a union of five integer intervals (each of the form [x 0 L d , x / L d ] ʝ [0, 255]) whose centers are the pending on the complexity of the class of images.…”

The convolution back projection algorithm based on windows function

“…INTRODUCTION T here are many scan modes in industrial computed tomography(also called ICT) [1], [2], [3], [4]. Therefore it is very necessary to study the related reconstruction algorithms [5] in ICT. The most mature algorithms are convolution back projection algorithm [5].…”

“…Therefore it is very necessary to study the related reconstruction algorithms [5] in ICT. The most mature algorithms are convolution back projection algorithm [5]. But the implementation of rearrangement algorithm is limited because it must satisfy some requirements in order to use it.…”

“…(2)Use Riemann approximation to compute the external integral of equation (3) to get: f *(r4 = Z m 21gI(a,mA) (5) Equation (4), (5) are software implementation formula for beam convolution back projection method. Because a may not be integral times of angle 2 , therefore g&W,mA) can be calculated from g,(nA,mA)by interpolation method [6], [7], [8].A is the rotation angle of graduation.…”