Jorma K. Merikoski

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The incorporation of nonnegativity constraints in image reconstruction problems is known to have a stabilizing effect on solution methods. In this paper, we both demonstrate and provide an explanation of this phenomena when the image reconstruction problem of interest has least squares form. The benefits of using this natural constraint suggest the(More)
We present an asymptotic formula for the number of line segments connecting q + 1 points of an n × n square grid, and a sharper formula, assuming the Riemann hypothesis. We also present asymptotic formulas for the number of lines through at least q points and, respectively, through exactly q points of the grid. The well-known case q = 2 is so generalized.
Given n ∈ Z, its arithmetic derivative n ′ is defined as follows: (i) 0 ′ = 1 ′ = (−1) ′ = 0. (ii) If n = up 1 · · · p k , where u = ±1 and p 1 ,. .. , p k are primes (some of them possibly equal), then n ′ = n k j=1 1 p j = u k j=1 p 1 · · · p j−1 p j+1 · · · p k. An analogous definition can be given in any unique factorization domain. What about the(More)