Inverse problems involve estimating an underlying continuous function from a set of measurements of some aspect of the function. The mapping from the underlying continuous function to the measurements is known as the forward or direct problem. The forward problem must be a well-posed physical problem. If x is an underlying function and y is a set of measurements, then x and y are related by a f...

Based on flexible pneumatic bending joint and flexible pneumatic spherical joint, a kind of flexible pneumatic 5-DOF finger is proposed, which is composed of two bending joints and a spherical joint. The mathematic model of flexible pneumatic spherical joint is further analyzed. On the researching foundation of flexible pneumatic bending joint and flexible pneumatic spherical joint, the kinemat...

in this paper, a nonlinear inverse problem of parabolic type, is considered. by reducing this inverse problem to a system of volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

The development of computational algorithms for solving inverse problems is, and has been, a primary focus of the inverse problems community. Less studied, but of increased interest, is uncertainty quantification for solutions of inverse problems obtained using computational methods. In this paper, we present a method of uncertainty quantification for linear inverse problems with nonnegativity ...

A method of inverse sampling of controls in a matched case-control study is described in which, for each case, controls are sampled until a discordant set is achieved. For a binary exposure, inverse sampling is used to determine the number of controls for each case. When most individuals in a population have the same exposure, standard case-control sampling may result in many case-control sets ...

We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the intensity vector over a large system of linear two-sided inequalities. The SM can be viewed conceptually as lying between feasibilityseeking for the constrai...

where A is some set of multiindices α. A first crucial question is whether there is enough data to (uniquely) find f . Let u0 be a function in the Sobolev space H(Ω) with zero Cauchy data u0 = ∂νu0 = 0 on Γ0 and let f0 = −∆u0. Due to linearity, −∆(u+ u0) = f + f0. Obviously, u and u+ u0 have the same Cauchy data on Γ0, so f and f+f0 produce the same data (2), but they are different in Ω. It is ...