An uncertainty inequality

作者：de Hoog Frank^*; Schmalz Gerd; Gureyev Tirnur E

来源：Applied Mathematics Letters, 2014, 38: 84-86.

DOI：10.1016/j.aml.2014.07.009

• Heisenberg inequality
• Imaging systems
• Noise resolution duality
• Spatial resolution
• Smoothing

Recently, the authors derived an uncertainty relationship between noise and spatial resolution in linear computational imaging systems that is similar to the Heisenberg uncertainty principle for conjugate variables in quantum mechanics. Specifically, for linear shift-invariant systems with a fixed incident photon density, the product of noise and spatial resolution has a positive absolute lower limit which can be evaluated with the aid of the inequality
parallel to g parallel to(a(p+1))(p+1) parallel to vertical bar x vertical bar(a)g parallel to(np)(1)/parallel to g parallel to(a(p+1)+np)(1) >= C(n, p, a), p > 0; a > 0,
where g is an element of L-1 (R-n) boolean AND L-1(R-n, vertical bar x vertical bar(a)) boolean AND Lp+1(R-n). This inequality, which is derived in this note, also has applications in data smoothing and in variations of Heisenberg's inequality.

• 出版日期2014-12