Application of the row action maximum likelihood algorithm with spherical basis functions to clinical PET imaging

2001 ◽  
Vol 48 (1) ◽  
pp. 24-30 ◽  
Author(s):  
M.E. Daube-Witherspoon ◽  
S. Matej ◽  
J.S. Karp ◽  
R.M. Lewitt
Keyword(s):  
Maximum Likelihood ◽  
Pet Imaging ◽  
Basis Functions ◽  
Maximum Likelihood Algorithm ◽  
Spherical Basis ◽  
Spherical Basis Functions

scholarly journals $L^p$ Bernstein estimates and approximation by spherical basis functions

2009 ◽  
Vol 79 (271) ◽  
pp. 1647-1679 ◽  
Author(s):  
H. N. Mhaskar ◽  
F. J. Narcowich ◽  
J. Prestin ◽  
J. D. Ward
Keyword(s):  
Basis Functions ◽  
Spherical Basis ◽  
Spherical Basis Functions

scholarly journals Interactive Generation of Path-Traced Lightmaps

2021 ◽  
Author(s):  
◽  
Thomas Roughton
Keyword(s):  
Real Time ◽  
Low Frequency ◽  
Basis Functions ◽  
Prior Work ◽  
Path Tracing ◽  
Spherical Basis ◽  
Real Time Applications ◽  
Indirect Illumination ◽  
Progressive Rendering ◽  
Spherical Basis Functions

<p>Indirect illumination is an important part of realistic images, and accurately simulating the complex effects of indirect illumination in real-time applications has long been a challenge for the industry. One popular approach is to use offline precomputed solutions such as lightmaps (textures containing the precomputed lighting in a scene) to efficiently approximate these effects. Unfortunately, these offline solutions have historically enforced long iteration times that come at a cost to artist productivity. These solutions have additionally either supported only the low-frequency diffuse component of indirect lighting, yielding poor visual results for glossy or metallic materials, or have used overly expensive approximations.  In recent years, the state of the art lightmap precomputation pipeline has shifted to using highly vectorised path tracing, often on GPU hardware, to compute the indirect illumination effects. The use of path tracing enables progressive rendering, wherein an approximation to the full solution is found and then refined as opposed to solving for the final result in a single step. Progressive rendering through path tracing thereby helps to provide rapid iteration for artists.  This thesis describes a system that can progressively path-trace indirect illumination lightmaps on the GPU.Contributing to this system, itintroduces a new gather-based method for sample accumulation, enhances algorithms from prior work, and presents a range of encoding methods, including a novel progressive method for non-negative least-squares encoding of spherical basis functions.  In addition, it presents a novel, efficient solution for high-quality precomputed diffuse and low-frequency specular indirect illumination that extends the Ambient Dice family of spherical basis functions. This solution provides comparable or better specular reconstruction to prior work at lower runtime cost and has potential for widespread use in real-time applications.</p>

scholarly journals Interactive Generation of Path-Traced Lightmaps

2021 ◽  
Author(s):  
◽  
Thomas Roughton
Keyword(s):  
Real Time ◽  
Low Frequency ◽  
Basis Functions ◽  
Prior Work ◽  
Path Tracing ◽  
Spherical Basis ◽  
Real Time Applications ◽  
Indirect Illumination ◽  
Progressive Rendering ◽  
Spherical Basis Functions

<p>Indirect illumination is an important part of realistic images, and accurately simulating the complex effects of indirect illumination in real-time applications has long been a challenge for the industry. One popular approach is to use offline precomputed solutions such as lightmaps (textures containing the precomputed lighting in a scene) to efficiently approximate these effects. Unfortunately, these offline solutions have historically enforced long iteration times that come at a cost to artist productivity. These solutions have additionally either supported only the low-frequency diffuse component of indirect lighting, yielding poor visual results for glossy or metallic materials, or have used overly expensive approximations.  In recent years, the state of the art lightmap precomputation pipeline has shifted to using highly vectorised path tracing, often on GPU hardware, to compute the indirect illumination effects. The use of path tracing enables progressive rendering, wherein an approximation to the full solution is found and then refined as opposed to solving for the final result in a single step. Progressive rendering through path tracing thereby helps to provide rapid iteration for artists.  This thesis describes a system that can progressively path-trace indirect illumination lightmaps on the GPU.Contributing to this system, itintroduces a new gather-based method for sample accumulation, enhances algorithms from prior work, and presents a range of encoding methods, including a novel progressive method for non-negative least-squares encoding of spherical basis functions.  In addition, it presents a novel, efficient solution for high-quality precomputed diffuse and low-frequency specular indirect illumination that extends the Ambient Dice family of spherical basis functions. This solution provides comparable or better specular reconstruction to prior work at lower runtime cost and has potential for widespread use in real-time applications.</p>

scholarly journals High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. Cabello ◽  
J. E. Gillam ◽  
M. Rafecas
Keyword(s):  
High Performance ◽  
Parallel Implementation ◽  
Computation Time ◽  
Basis Functions ◽  
Image Space ◽  
System Response ◽  
Processing Unit ◽  
Central Processing ◽  
Spherical Basis ◽  
Spherical Basis Functions

Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by exploiting spherical symmetries, although computation time is still slower compared to non-overlapping basis functions. In this work, we have implemented the reconstruction algorithm using Graphical Processing Unit (GPU) technology for speed and a precomputed Monte-Carlo-calculated SRM for accuracy. The reconstruction time achieved using spherical basis functions on a GPU was 4.3 times faster than the Central Processing Unit (CPU) and 2.5 times faster than a CPU-multi-core parallel implementation using eight cores. Overwriting hazards are minimized by combining a random line of response ordering and constrained atomic writing. Small differences in image quality were observed between implementations.

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