2011/08/08 by Karthik S. Gurumoorthy, Gurumoorthy, Karthik S., Anand Rangarajan +3
Decision Sciences · Environmental Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Probabilistic and Robust Engineering Design #Soil Geostatistics and Mapping #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1108.1783
openalex publication_date 2011/08/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We prove a novel result wherein the density function of the gradients---corresponding to density function of the derivatives in one dimension---of a thrice differentiable function S (obtained via a random variable transformation of a uniformly distributed random variable) defined on a closed, bounded interval Ω⊂ R is accurately approximated by the normalized power spectrum of ϕ=exp(iS/τ) as the free parameter τ-->0. The result is shown using the well known stationary phase approximation and standard integration techniques and requires proper ordering of limits. Experimental results provide anecdotal visual evidence corroborating the result.