Oleg Tischenko

A new reconstruction algorithm for Radon data

A new reconstruction algorithm for Radon data is introduced. We call the new algorithm OPED as it is based on Orthogonal Polynomial Expansion on the Disk. OPED is fundamentally different from the filtered back projection (FBP) method. It allows one to use fan beam geometry directly without any additional procedures such as interpolation or rebinning. It reconstructs high degree polynomials exactly and works for smooth functions without the assumption that functions are band- limited. Our initial tests indicate that the algorithm is stable, provides high resolution images, and has a small global error. Working with the geometry specified by the algorithm and a new mask, OPED could also lead to a reconstruction method that works with reduced x-ray dose (see the paper by Tischenko et al in these proceedings).

An artifact-free structure-saving noise reduction using the correlation between two images for threshold determination in the wavelet domain

A new method of noise reduction based on shrinkage in the wavelet domain has been created for the application in projection radiography. The method is based on comparing two similar or quasi-identical images of the same object. Using an appropriate measure of similarity, these images are compared with each other in order to produce the weighting matrices. The weighting factors for the wavelet coefficients are chosen to be proportional to the elements of the weighting matrices. One image of the pair is then reconstructed from the weighted wavelet coefficients. The effect of this kind of de-noising is a suppression of those structures in the image which don’t correlate with the structures in the other image of the pair. Normally the suppressed structures are quantum or scatter noise, while the correlated structures which are not affected at all, are the real anatomical structures.

Image reconstruction by OPED algorithm with averaging

OPED is a new image reconstruction algorithm based on orthogonal polynomial expansion on the disk. We show that the integral of the approximation function in OPED can be given explicitly and evaluated efficiently. As a consequence, the reconstructed image over a pixel can be effectively represented by its average over the pixel, instead of by its value at a single point in the pixel, which can help to reduce the aliasing caused by under sampling. Numerical examples are presented to show that the averaging process indeed improves the quality of the reconstructed images.

Investigation of image components affecting the detection of lung nodules in digital chest radiography

The aim of this work was to investigate and quantify the effects of system noise, nodule location, anatomical noise and anatomical background on the detection of lung nodules in different regions of the chest x-ray. Simulated lung nodules of diameter 10 mm but with varying detail contrast were randomly positioned in four different kinds of images: 1) clinical images collected with a 200 speed CR system, 2) images containing only system noise (including quantum noise) at the same level as the clinical images, 3) clinical images with removed anatomical noise, 4) artificial images with similar power spectrum as the clinical images but random phase spectrum. An ROC study was conducted with 5 observers. The detail contrast needed to obtain an Az of 0.80, C0.8, was used as measure of detectability. Five different regions of the chest x-ray were investigated separately. The C0.8 of the system noise images ranged from only 2% (the hilar regions) to 20% (the lateral pulmonary regions) of those of the clinical images. Compared with the original clinical images, the C0.8 was 16% lower for the de-noised clinical images and 71% higher for the random phase images, respectively, averaged over all five regions. In conclusion, regarding the detection of lung nodules with a diameter of 10 mm, the system noise is of minor importance at clinically relevant dose levels. The removal of anatomical noise and other noise sources uncorrelated from image to image leads to somewhat better detection, but the major component disturbing the detection is the overlapping of recognizable structures, which are, however, the main aspect of an x-ray image.

Measurement of the noise components in the medical x-ray intensity pattern due to overlaying nonrecognizable structures

There are many aspects that influence and deteriorate the detection of pathologies in X-ray images. Some of those are due to effects taking place in the stage of forming the X-ray intensity pattern in front of the x-ray detector. These can be described as motion blurring, depth blurring, anatomical background, scatter noise and structural noise. Structural noise results from an overlapping of fine irrelevant anatomical structures. A method for measuring the combined effect of structural noise and scatter noise was developed and will be presented in this paper. This method is based on the consideration that within a pair of projections created after rotation of the object with a small angle (which is within the typical uncertainty in positioning the patient) both images would show the same relevant structures whereas the projection of the fine overlapping structures will appear quite differently in the two images. To demonstrate the method two X-ray radiographs of a lung phantom were produced. The second radiograph was achieved after rotating the lung by an angle of about 3. Dyadic wavelet representations of both images were regarded. For each value of the wavelet scale parameter the corresponding pair of approximations was matched using the cross correlation matching technique. The homologous regions of approximations were extracted. The image containing only those structures that appear in both images simultaneously was then reconstructed from the wavelet coefficients corresponding to the homologous regions. The difference between one of the original images and the noise-reduced image contains the structural noise and the scatter noise.

A new scanning device in CT with dose reduction potential

The amount of x-ray radiation currently applied in CT practice is not utilized optimally. A portion of radiation traversing the patient is either not detected at all or is used ineffectively. The reason lies partly in the reconstruction algorithms and partly in the geometry of the CT scanners designed specifically for these algorithms. In fact, the reconstruction methods widely used in CT are intended to invert the data that correspond to ideal straight lines. However, the collection of such data is often not accurate due to likely movement of the source/detector system of the scanner in the time interval during which all the detectors are read. In this paper, a new design of the scanner geometry is proposed that is immune to the movement of the CT system and will collect all radiation traversing the patient. The proposed scanning design has a potential to reduce the patient dose by a factor of two. Furthermore, it can be used with the existing reconstruction algorithm and it is particularly suitable for OPED, a new robust reconstruction algorithm.

Approximation and Reconstruction from Attenuated Radon Projections

Attenuated Radon projections with respect to the weight function

Main features of the tomographic reconstruction algorithm OPED

W_\mu(x,y) = (1-x^2-y^2)^{\mu-1/2}

Experimental proof of an idea for a CT-scanner with dose reduction potential

are shown to be closely related to the orthogonal expansion in two variables with respect to

Modeling and testing of a non-standard scanning device with dose reduction potential

W_\mu