Development of iterative reconstruction methods

PET Reconstruction Software Toolkit (PRESTO) – A flexible C++ Library for iterative, fully 3D PET Image Reconstruction

PET images reconstructed by iterative methods, such as the maximum likelihood expectation maximisation (MLEM) or ordered subset expectation maximisation (OSEM) algorithms, exhibit a favourable signal-to-noise ratio compared to results of filtered back projection, especially in the case of studies with low counts. Since the iterative methods are computationally time-consuming in general, they are often implemented in a compromising way to achieve acceptable computation times. Therefore, in order to realise a direct LOR reconstruction with an optimal image quality, our group has developed the PET Reconstruction Software Toolkit (PRESTO). The C++ library PRESTO demonstrates the possibility of avoiding any LOR reduction strategy and using more appropriate, but computationally demanding, Volumes-of-Intersection projectors [1] to significantly improve image quality [2]. The new framework is explicitly based on specific non-Cartesian voxel patterns with multiple polar symmetries, to strongly enhance the amount of exploitable symmetries. In contrast to classical Cartesian voxel patterns, a much higher degree of symmetry and related matrix redundancy result in a very high matrix compression. Compression factors above 300 can be easily exceeded, thus allowing the complete storage of the SRM in Random Access Memory (RAM). Consequently, the time required to calculate the SRM has no influence on the image reconstruction time. This approach implies an advantage against conventional on-the-fly calculations. Furthermore, PRESTO has the capability of ultra-fast image reconstruction due to the use of efficient, symmetry-driven data vectorisation [3]. For example, the LOR reconstruction of the Siemens BrainPET scanner hosted at our site takes less than 3 minutes on a single high-end machine while taking all 230 million physical LORs independently into account [4].

In addition, to optimise scanner-specific, direct LOR reconstructions PRESTO also enables flexible, scanner-independent storage and reconstruction of tomographic projection data from any type of PET detector geometry, without using the concept of 2D/3D sinograms. Instead, a cylinder surface is subdivided into generic rings (axial) and each ring into generic detector surfaces (transaxial) as smallest entities. Basic geometrical parameters determining the sampling granularity are user-definable: cylinder diameter, length of the axial field-of-view, number of crystals per ring and number of rings. Thus, all combinations of generic detector surfaces completely sample the projection space in terms of Tubes-of-Response (TOR) spanned by any two surfaces. This concept allows the realisation of a highly compressed, memory-resident SRM for any kind of detector geometry.