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Comparison of Haar wavelet-based and Poisson-based numerical integration techniques

This paper shows performance and computation trade-offs of two approaches to 2-D numerical integration. The speed of convergence on a digital photograph is shown for the Jacobi-based Poisson algorithm. The alternate approach shown in this paper is one that solves for the Haar wavelet decomposition directly from gradient measurements. Then the image is obtained from this estimate of the decomposition. Finally, the same Poisson algorithm is performed on this wavelet approach to improve the results. The intended application of these approaches is to determine the image associated with gradient measurements when the image itself is unknown.