Stochastic methods for joint registration, restoration, and interpolation of multiple undersampled images

Abstract

Using a stochastic framework, we propose two algorithms for the problem of obtaining a single high-resolution image from multiple noisy, blurred, and undersampled images. The first is based on a Bayesian formulation that is implemented via the expectation maximization algorithm. The second is based on a maximum a posteriori formulation. In both of our formulations, the registration, noise, and image statistics are treated as unknown parameters. These unknown parameters and the high-resolution image are estimated jointly based on the available observations. We present an efficient implementation of these algorithms in the frequency domain that allows their application to large images. Simulations are presented that test and compare the proposed algorithms.

Optimal Registration Of Aliased Images Using Variable Projection With Applications To Super-Resolution

“…The algorithmic efficiency is achieved due to fast and memory efficient inversion of the matrices in the Fourier domain. We note that the efficiency of treating the problem in the Fourier domain has been noted previously [11,14,31].…”

“…It is this equation that the authors of [8,11,24] attempt to minimize using iterative cyclic coordinate descent type algorithms.…”

“…Thinking about the problem in this way offers a statistically justifiable approach to separating the problem of estimating x from that of jointly estimating the blurred high-resolution image z and the unknown motion parameters v. Under certain scenarios, this presents a natural alternative to the more complex coordinate descent approach of [11], where the coordinate descent optimization is employed to estimate the motion parameters, high-resolution image, blur operator and noise power. As shown in [19], when a sufficient number of frames are available, the estimation of fz, vg is often well conditioned.…”

“…The second class of algorithms combine the registration problem into the super-resolution estimation problem [8,11,24]. In [19], such a joint method was shown to be statistically optimal.…”

“…In [19], such a joint method was shown to be statistically optimal. To date, all of these algorithms use some form of cyclic coordinate descent or a form of the Expectation -Maximization (EM) algorithm [11,24]. Such algorithms iterate between estimating the high-resolution image x (expectation step) and the set of unknown motion parameters (maximization step).…”