Nonlinear and Nonideal Sampling: Theory and Methods

Abstract

Abstract-We study a sampling setup where a continuous-time signal is mapped by a memoryless, invertible and nonlinear transformation, and then sampled in a nonideal manner. Such scenarios appear, for example, in acquisition systems where a sensor introduces static nonlinearity, before the signal is sampled by a practical analog-to-digital converter. We develop the theory and a concrete algorithm to perfectly recover a signal within a subspace, from its nonlinear and nonideal samples. Three alternative formulations of the algorithm are described that provide different insights into the structure of the solution: A series of oblique projections, approximated projections onto convex sets, and quasi-Newton iterations. Using classical analysis techniques of descent-based methods, and recent results on frame perturbation theory, we prove convergence of our algorithm to the true input signal. We demonstrate our method by simulations, and explain the applicability of our theory to Wiener-Hammerstein analog-to-digital hybrid systems.

Motion blur removal in nonlinear sensors

“…The approach we present in this paper relies on a recently developed theory for nonlinear sampling. 13 Specifically, the intensity values measured at a certain location in the image sensor correspond to nonindeal samples (due to the nonzero integration time) of a nonlinearly distorted version (due to the sensor's nonlinearity) of the continuous-time intensity that impinged on the corresponding location in the sensor. Thus, we propose a NCMD algorithm that recovers the continuous-time intensity corresponding to each of the pixels in the video independently.…”

“…Thus, we propose a NCMD algorithm that recovers the continuous-time intensity corresponding to each of the pixels in the video independently. As shown in, 13 this is possible under certain mild assumptions on the temporal changes in the continuous-time pixel intensities and on the nonlinearity. We propose using the iterative algorithm developed in 14 for this task.…”

“…13 This method was later on revised to be faster and easier to implement. 14 In this section we briefly describe the recovery algorithm, 14 summarize the guarantees for its success, and show how it relates to the NCMD problem.…”

Block sparsity and sampling over a union of subspaces

“…Here x, y denotes the standard inner product on H. Nonlinear sampling is treated in [29]. However, here our focus will be on the linear case.…”

Nonlinear and Nonideal Sampling Revisited

“…Nonlinear distortions appear in various setups and applications of digital signal processing, such as CCD image sensors, power electronics and radiometric photography (see [1] and references therein).…”