We present two results characterizing minimizers of the Chan-Esedoḡlu LTV functional F (u) ≡ ∫ |∇u|dx + λ ∫ |u − f |dx; u, f : R → R. If we restrict to u = χΣ and f = χΩ, Σ,Ω ∈ R, the LTV functional reduces to E(Σ) = Per(Σ) + λ|Σ M Ω|. We show that there is a minimizer Σ such that its boundary ∂Σ lies between the union of all balls of radius nλ contained in Ω and the corresponding union of n λ ...

This research uses a dual attitudes perspective to offer new insights into flattery and its consequences. The authors show that even when flattery by marketing agents is accompanied by an obvious ulterior motive that leads targets to discount the proffered compliments, the initial favorable reaction (the implicit attitude) continues to coexist with the discounted evaluation (the explicit attitu...

We consider the image reconstruction problem when the original image is assumed to be sparse and when partial knowledge of the point spread function (PSF) is available. In particular, we are interested in recovering the magnetization density given magnetic resonance force microscopy (MRFM) data, and we present an iterative alternating minimization algorithm (AM) to solve this problem. A smoothi...