Global-Scale Three-Dimensional Statistical Estimation

In the statistical estimation context, the difficulty in the transition from two– to three-dimensional problems is much more than an increase in the number of pixels: the complexity per pixel is cubed!, even for efficient estimation algorithms. That is, even aside from the other challenges posed by 3D estimation (e.g., complex data structures, the difficulty of determining empirical statistics), the computational issues alone are significant and merit attention. This paper introduces an alternative approach, motivated by multiscale estimation and the multipole algorithm of mathematical physics.