Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation

Abstract

Abstract-Many material and biological samples in scientific imaging are characterized by non-local repeating structures. These are studied using scanning electron microscopy and electron tomography. Sparse sampling of individual pixels in a 2D image acquisition geometry, or sparse sampling of projection images with large tilt increments in a tomography experiment, can enable high speed data acquisition and minimize sample damage caused by the electron beam.In this paper, we present an algorithm for electron tomographic reconstruction and sparse image interpolation that exploits the non-local redundancy in images. We adapt a framework, termed plug-and-play (P&P) priors, to solve these imaging problems in a regularized inversion setting. The power of the P&P approach is that it allows a wide array of modern denoising algorithms to be used as a "prior model" for tomography and image interpolation. We also present sufficient mathematical conditions that ensure convergence of the P&P approach, and we use these insights to design a new non-local means denoising algorithm. Finally, we demonstrate that the algorithm produces higher quality reconstructions on both simulated and real electron microscope data, along with improved convergence properties compared to other methods.Index Terms-Plug-and-play, prior modeling, bright field electron tomography, sparse interpolation, non-local means, doublystochastic gradient non-local means, BM3D.

Sparse superresolution phase retrieval from phase-coded noisy intensity patterns

“…(9)- (10) is in line with the recent concept plug-and-play, [45][46][47] stating that any efficient filter can serve as a potentially good prior and efficient regularizator in variational design of data processing algorithms.…”

Discriminative Transfer Learning for General Image Restoration

“…Plug-and-play priors ( [31], [32], [33], [43]): Like the plug-and-play work, our method uses formal optimization with a proximal operator framework. However, while plug-and-play methods adopt an existing generic Gaussian denoiser for the prior proximal operator, our method trains the prior proximal operator with discriminative learning technique.…”

“…We notice that recent plug-and-play work [31], [32], [33] adopt similar proximal splitting strategy as our method though with the ADMM framework. However, while plug-and-play methods adopt existing generic Gaussian denoiser for the prior proximal operator, our method trains the prior proximal operator and other parameters used in the optimization algorithm with discriminative learning technique.…”

“…Another line of research, which is closely related to our approach, is the plug-and-play technique [31], [32], [33], [34]. In these methods, Gaussian denoisers are utilized as image regularizers for solving general inverse problems, through splitting optimization methods such as ADMM [12].…”

Image Restoration with Multiple Hard Constraints on Data-Fidelity to Blurred/Noisy Image Pair

“…In this case, R is the 1 norm, and Ψ is a frame analysis operator, e.g., wavelet [30] and curvelet [31]. More involved regularization, such as nonlocal regularization [32]- [34], regularization using learned operators [35], [36] and plug-and-play regularization [37], [38], can also be handled in our formulation by setting Ψ to the corresponding nonlocal/learned analysis operator.…”