Transport-based model for turbulence-corrupted imagery

Abstract

A new model for turbulence-corrupted imagery is proposed based on the theory of optimal mass transport. By describing the relationship between photon density and the phase of the traveling wave, and combining it with a least action principle, the model suggests a new class of methods for approximately recovering the solution of the photon density flow created by a turbulent atmosphere. Both coherent and incoherent imagery are used to validate and compare the model to other methods typically used to describe this type of data. Given its superior performance in describing experimental data, the new model suggests new algorithms for a variety of atmospheric imaging and wave propagation applications.

Parametric Signal Estimation Using the Cumulative Distribution Transform

“…Such models are common in wave optics, for example, where Eqn. ( 1) is seen to operate on the squared magnitude of a wavefunction or an electric field (see e.g., Schrodinger equation [12] or paraxial wave equation [13,14]). For example, if s(t) represents the time-varying optical intensity of a beam propagating through a lossless medium, g p (t) captures the influence of the medium to yield the modified intensity s g (t) [11].…”

Approximate solutions for propagating light beams in a material with quadratic, exponential, and quartic transverse refractive index profiles

“…is the change in transverse location (i.e. transverse optical path) per unit change in the direction of propagation (see again [24]). Thus, ( )…”

“…, can be viewed as a transverse velocity (a term also adopted in [25]), governing how the field intensity is moved in the transverse plane by the refractive index variations. Thus, in going from (1) to (2) we have transformed the problem from a single complex partial differential equation (PDE) to two real-valued PDEs (see also [24]).…”

Blind atmospheric turbulence deconvolution

“…In [21], Lau et al proposed to minimise a functional, using different regularisation terms, to perform specific subsampling of frames without any registration. A procedure based on optimal transport has been proposed in [22]. Several similar methods also use the strategy of combining a registration step with a deconvolution step, see for instance [23–27].…”