On the Superresolution Capacity of Imagers Using Unknown Speckle Illuminations

Abstract

Speckle based imaging consists of forming a superresolved reconstruction of an unknown sample from lowresolution images obtained under random inhomogeneous illuminations (speckles). In a blind context where the illuminations are unknown, we study the intrinsic capacity of speckle-based imagers to recover spatial frequencies outside the frequency support of the data, with minimal assumptions about the sample.We demonstrate that, under physically realistic conditions, the covariance of the data has a super-resolution power corresponding to the squared magnitude of the imager point spread function. This theoretical result is important for many practical imaging systems such as acoustic and electromagnetic tomographs, fluorescence and photoacoustic microscopes, or synthetic aperture radar imaging. A numerical validation is presented in the case of fluorescence microscopy.

Double moiré localized plasmon structured illumination microscopy

“…This implies that reconstruction algorithms are confined to be blind, i.e., to those that recognize the object at the same time as the illumination. A problem with blind-SIM reconstruction is that it can be shown that without any a priori assumptions about the experiment, blind-SIM can not recover illumination spatial frequencies higher than the frequency cutoff k cutoff [49]. Therefore, to make full use of the plasmonic illumination for the resolution enhancement, additional a priori information such as sparsity or frequency content needs to be utilized during the reconstruction process.…”

Computational Super-Sectioning for Single-Slice Structured-Illumination Microscopy

“…These components can then be numerically recovered and shifted back to their correct location to produce an image with twice the resolution of conventional systems. This twofold resolution enhancement can also be obtained using speckle illuminations [6] and, theoretically, unlimited resolution can even be achieved from nonlinear SIM [7], such as the saturated-SIM that was originally introduced in [8], [9].…”

Random Illumination Microscopy from Variance Images

“…RIM consists in shining the sample with several uncontrolled speckles and in extracting a super-resolved image from the multiple low frequency images acquired. The maximum super-resolution gain of RIM is the same as SIM [7], i.e., a factor of two in the lateral dimensions. On the other hand, RIM requires only simple modifications of a fluorescent microscope, and it is easy to use [8].…”

“…Such a method is asymptotically consistent [11], and it does not rely on a prior knowledge about the quantity of interest. In [7], a Kullback Leibler divergence is used as a contrast function between the empirical and statistical second order moments. However, this estimator relies on image covariance matching, which has a prohibitive cost of O(N 2 ) and O(N 3 ) in terms of memory and CC for N -pixel images, respectively.…”