Closed-Form Projection Method for Regularizing a Function Defined by a\n Discrete Set of Noisy Data and for Estimating its Derivative and Fractional\n Derivative

2018/05/24 by Timothy J. Burns, Burns, Timothy J., Bert W. Rust +1
Mathematics · Computer Science · #Numerical methods in inverse problems #Statistical and numerical algorithms #Image and Signal Denoising Methods

paper · pdf · doi:10.48550/arxiv.1805.09849

Abstract

We present a closed-form finite-dimensional projection method for\nregularizing a function defined by a discrete set of measurement data, which\nhave been contaminated by random, zero mean errors, and for estimating the\nderivative and fractional derivative of this function by linear combinations of\na few low degree trigonometric or Jacobi polynomials. Our method takes\nadvantage of the fact that there are known infinite-dimensional singular value\ndecompositions of the operators of integration and fractional integration.\n

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