Evaluation of non-Gaussian statistical properties in virtual breast phantoms

Images derived from a "virtual phantom" can be useful in characterizing the performance of imaging systems. This has driven the development of virtual breast phantoms implemented in simulation environments. In breast imaging, several such phantoms have been proposed. We analyze the non-Gaussian statistical properties from three classes of virtual breast phantoms and compare them to similar statistics from a database of breast images. These include clustered-blob lumpy backgrounds (CBLBs), truncated binary textures, and the UPenn virtual breast phantoms. We use Laplacian fractional entropy (LFE) as a measure of the non-Gaussian statistical properties of each simulation procedure. Our results show that, despite similar power spectra, the simulation approaches differ considerably in LFE with very low scores for the CBLB to high values for the UPenn phantom at certain frequencies. These results suggest that LFE may have value in developing and tuning virtual phantom simulation procedures.

Modeling of laser-induced breakdown spectroscopic data analysis by an automatic classifier

Laser-induced breakdown spectroscopy (LIBS) is a multi-elemental and real-time analytical technique with simultaneous detection of all the elements in any type of sample matrix including solid, liquid, gas, and aerosol. LIBS produces vast amount of data which contains information on elemental composition of the material among others. Classification and discrimination of spectra produced during the LIBS process are crucial to analyze the elements for both qualitative and quantitative analysis. This work reports the design and modeling of optimal classifier for LIBS data classification and discrimination using the apparatus of statistical theory of detection. We analyzed the noise sources associated during the LIBS process and created a linear model of an echelle spectrograph system. We validated our model based on assumptions through statistical analysis of "dark signal" and laser-induced breakdown spectra from the database of National Institute of Science and Technology. The results obtained from our model suggested that the quadratic classifier provides optimal performance if the spectroscopy signal and noise can be considered Gaussian.

Description and characterization of a novel method for partial volume simulation in software breast phantoms

A modification to our previous simulation of breast anatomy is proposed to improve the quality of simulated x-ray projections images. The image quality is affected by the voxel size of the simulation. Large voxels can cause notable spatial quantization artifacts; small voxels extend the generation time and increase the memory requirements. An improvement in image quality is achievable without reducing voxel size by the simulation of partial volume averaging in which voxels containing more than one simulated tissue type are allowed. The linear x-ray attenuation coefficient of voxels is, thus, the sum of the linear attenuation coefficients weighted by the voxel subvolume occupied by each tissue type. A local planar approximation of the boundary surface is employed. In the two-material case, the partial volume in each voxel is computed by decomposition into up to four simple geometric shapes. In the three-material case, by application of the Gauss-Ostrogradsky theorem, the 3D partial volume problem is converted into one of a few simpler 2D surface area problems. We illustrate the benefits of the proposed methodology on simulated x-ray projections. An efficient encoding scheme is proposed for the type and proportion of simulated tissues in each voxel. Monte Carlo simulation was used to evaluate the quantitative error of our approximation algorithms.

Optimized generation of high resolution breast anthropomorphic software phantoms

PURPOSE

The authors present an efficient method for generating anthropomorphic software breast phantoms with high spatial resolution. Employing the same region growing principles as in their previous algorithm for breast anatomy simulation, the present method has been optimized for computational complexity to allow for fast generation of the large number of phantoms required in virtual clinical trials of breast imaging.

METHODS

The new breast anatomy simulation method performs a direct calculation of the Cooper's ligaments (i.e., the borders between simulated adipose compartments). The calculation corresponds to quadratic decision boundaries of a maximum a posteriori classifier. The method is multiscale due to the use of octree-based recursive partitioning of the phantom volume. The method also provides user-control of the thickness of the simulated Cooper's ligaments and skin.

RESULTS

Using the proposed method, the authors have generated phantoms with voxel size in the range of (25-1000 μm)(3)∕voxel. The power regression of the simulation time as a function of the reciprocal voxel size yielded a log-log slope of 1.95 (compared to a slope of 4.53 of our previous region growing algorithm).

CONCLUSIONS

A new algorithm for computer simulation of breast anatomy has been proposed that allows for fast generation of high resolution anthropomorphic software phantoms.