Computerized image reconstruction methods with multiple photon/x-ray transmission scanning

Performance of principal component analysis and independent component analysis with respect to signal extraction from noisy positron emission tomography data - a study on computer simulated images

Multivariate image analysis tools are used for analyzing dynamic or multidimensional Positron Emission Tomography, PET data with the aim of noise reduction, dimension reduction and signal separation. Principal Component Analysis is one of the most commonly used multivariate image analysis tools, applied on dynamic PET data. Independent Component Analysis is another multivariate image analysis tool used to extract and separate signals. Because of the presence of high and variable noise levels and correlation in the different PET images which may confound the multivariate analysis, it is essential to explore and investigate different types of pre-normalization (transformation) methods that need to be applied, prior to application of these tools. In this study, we explored the performance of Principal Component Analysis (PCA) and Independent Component Analysis (ICA) to extract signals and reduce noise, thereby increasing the Signal to Noise Ratio (SNR) in a dynamic sequence of PET images, where the features of the noise are different compared with some other medical imaging techniques. Applications on computer simulated PET images were explored and compared. Application of PCA generated relatively similar results, with some minor differences, on the images with different noise characteristics. However, clear differences were seen with respect to the type of pre-normalization. ICA on images normalized using two types of normalization methods also seemed to perform relatively well but did not reach the improvement in SNR as PCA. Furthermore ICA seems to have a tendency under some conditions to shift over information from IC1 to other independent components and to be more sensitive to the level of noise. PCA is a more stable technique than ICA and creates better results both qualitatively and quantitatively in the simulated PET images. PCA can extract the signals from the noise rather well and is not sensitive to type of noise, magnitude and correlation, when the input data are correctly handled by a proper pre-normalization. It is important to note that PCA as inherently a method to separate signal information into different components could still generate PC1 images with improved SNR as compared to mean images.

Ultra fast symmetry and SIMD-based projection-backprojection (SSP) algorithm for 3-D PET image reconstruction

Remarkable progress in positron emission tomography (PET) development has occurred in recent years, in hardware, software, and computer implementation of image reconstruction. Recent development in PET scanners such as the high-resolution research tomograph (HRRT) developed by CTI (now Siemens) represents such a case and is capable of greatly enhanced resolution as well as sensitivity. In these PET scanners, the amount of coincidence line data collected contains more than 4.5 x 10(9) coincidence lines of response generated by as many nuclear detectors as 120 000. This formidable amount of data and the reconstruction of this data set pose a real problem in HRRT and have also been of the major bottle neck in further developments of high resolution PET scanners as well as their applications. In these classes of PET scanners, therefore, obtaining one set of reconstructed images often requires many hours of image reconstruction. For example, in HRRT with full data collection in a normal brain scan (using SPAN 3), the image reconstruction time is close to 80 min, making it practically impossible to attempt any list-mode-based dynamic imaging since the image reconstruction time would take many days (as much as 43 h or more for 32-frame dynamic image reconstruction). To remedy this data-handling problem in image reconstruction, we developed a new algorithm based on the symmetry properties of the projection and backprojection processes, especially in the 3-D OSEM algorithm where multiples of projection and back-projection are required. In addition, the single-instruction multiple-data (SIMD) technique also allowed us to successfully incorporate the symmetry properties mentioned above, thereby effectively reducing the total image reconstruction time to a few minutes. We refer to this technique as the symmetry and SIMD-based projection-backprojection (SSP) technique or algorithm and the details of the technique will be discussed and an example of the application of the technique to the HRRT's OSEM algorithm will be presented as a demonstration.

Non-isotropic noise correlation in PET data reconstructed by FBP but not by OSEM demonstrated using auto-correlation function

Background

Positron emission tomography (PET) is a powerful imaging technique with the potential of obtaining functional or biochemical information by measuring distribution and kinetics of radiolabelled molecules in a biological system, both in vitro and in vivo. PET images can be used directly or after kinetic modelling to extract quantitative values of a desired physiological, biochemical or pharmacological entity. Because such images are generally noisy, it is essential to understand how noise affects the derived quantitative values. A pre-requisite for this understanding is that the properties of noise such as variance (magnitude) and texture (correlation) are known.

Methods

In this paper we explored the pattern of noise correlation in experimentally generated PET images, with emphasis on the angular dependence of correlation, using the autocorrelation function (ACF). Experimental PET data were acquired in 2D and 3D acquisition mode and reconstructed by analytical filtered back projection (FBP) and iterative ordered subsets expectation maximisation (OSEM) methods. The 3D data was rebinned to a 2D dataset using FOurier REbinning (FORE) followed by 2D reconstruction using either FBP or OSEM. In synthetic images we compared the ACF results with those from covariance matrix. The results were illustrated as 1D profiles and also visualized as 2D ACF images.

Results

We found that the autocorrelation images from PET data obtained after FBP were not fully rotationally symmetric or isotropic if the object deviated from a uniform cylindrical radioactivity distribution. In contrast, similar autocorrelation images obtained after OSEM reconstruction were isotropic even when the phantom was not circular. Simulations indicated that the noise autocorrelation is non-isotropic in images created by FBP when the level of noise in projections is angularly variable. Comparison between 1D cross profiles on autocorrelation images obtained by FBP reconstruction and covariance matrices produced almost identical results in a simulation study.

Conclusion

With asymmetric radioactivity distribution in PET, reconstruction using FBP, in contrast to OSEM, generates images in which the noise correlation is non-isotropic when the noise magnitude is angular dependent, such as in objects with asymmetric radioactivity distribution. In this respect, iterative reconstruction is superior since it creates isotropic noise correlations in the images.

A new silent magnetic resonance imaging using a rotating DC gradient

A new approach to silent MR imaging using a rotating DC gradient has been explored and experimentally studied. Acoustic or sound noise has been one of the problems in examining patients, mainly due to the fast gradient pulsings in interaction with the main magnetic field. The sound noise has been noted to be proportionately louder as the magnetic field strength becomes larger. In this report, we describe a new imaging technique using a mechanically rotating DC gradient coil. The rotating DC gradient coil can effectively replace both phase encoding as well as readout gradient pulsings, and data obtained in this manner can provide a set of projection data that later can be used for projection reconstruction. With some interpolation techniques one can also perform conventional two-dimensional fast Fourier transform image reconstruction. The sound noise intensity compared with the conventional imaging technique, such as the spin-echo sequence, has been reduced down to about -20.7 dB or 117.5 times with this new technique. The experimental pulse sequence and its principle are described and images obtained by the new silent MR imaging technique are reported.

Physics of contrast mechanism and averaging effect of linear attenuation coefficients in a computerized transverse axial tomography CTAT) transmission scanner

Detailed studies of the basic contrast mechanisms in computerized transverse axial tomography scanners have been carried out. Contrast is related to the effective atomic numbers and electron densities of materials and the resultant linear attenuation coefficients. We have therefore quantitatively evaluated various samples defined by these parameters. A multienergetic X-ray source causes resolution degrading problems arising from the averaging effect of the linear attenuation coefficients. The controversy regarding the use of fixed length water bath as a reference to compensate the spectral shift (hardening) effect of the multienergetic X-ray source is also analysed and reported. Computer simulations demonstrating the sensitivities of the linear attenuation coefficient measurements and errors, as functions of the energy spectrum, were made for representative cases. Simulation results indicate that by using a full water bath, artifacts stemming from the multienergetic X-ray souce can be significantly reduced. An alternative approach using a count rate equalizer, considered to be another way of reducing the wide dynamic range in count rate when a water bath is not used, is also studied and the results reported.

Correction functions for optimizing the reconstructed image in transverse section scan

Two correction functions are derived for one- and two-dimensional convolution methods for reconstructing a section image from multiple projections. The functions are optimized to yield a maximum 'signal-to-noise power ratio' for a given RMS resolution width, where 'signal power' is the integrated squared line spread function (signal power regarding one-dimensional position information per count) and 'noise power' is the variance of the image density at the centre of a locally uniform source. The point spread function of the reconstructed image is Gaussian, and the standard deivation of noise associated with a locally uniform image is found to be proportional to D-3/2, where D is the RMS resolution width. The autocovariance function for uniform noise is also given.