Integer-valued images can be uniquely recovered from a minimal set of DFT coefficients through algebraic reduction to 1D problems and dynamic programming algorithms that use lattice approximation to handle NP-hard subproblems.
Probability density function of the Cartesian x-coordinate of the random point inside the hypersphere
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abstract
Consider randomly picked points inside the n-dimensional unit hypersphere centered at the origin of the Cartesian coordinate system. The Cartesian coordinates of the points are random variables, which form an n-dimensional vector for each point. Observing only the x-coordinate I obtained its probability density function (PDF). I show that it is related to the Gaussian distribution: in limit its companion PDF?? converges to the PDF of the standard normal distribution.
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2025 1verdicts
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Recovery of Integer Images from Minimal DFT Measurements: Uniqueness and Inversion Algorithms
Integer-valued images can be uniquely recovered from a minimal set of DFT coefficients through algebraic reduction to 1D problems and dynamic programming algorithms that use lattice approximation to handle NP-hard subproblems.