Soft thresholding schemes for multiple signal classification algorithm

Multiple signal classification algorithm (MUSICAL) exploits temporal fluctuations in fluorescence intensity to perform super-resolution microscopy by computing the value of a super-resolving indicator function across a fine sample grid. A key step in the algorithm is the separation of the measurements into signal and noise subspaces, based on a single user-specified parameter called the threshold. The resulting image is strongly sensitive to this parameter and the subjectivity arising from multiple practical factors makes it difficult to determine the right rule of selection. We address this issue by proposing soft thresholding schemes derived from a new generalized framework for indicator function design. We show that the new schemes significantly alleviate the subjectivity and sensitivity of hard thresholding while retaining the super-resolution ability. We also evaluate the trade-off between resolution and contrast and the out-of-focus light rejection using the various indicator functions. Through this, we create significant new insights into the use and further optimization of MUSICAL for a wide range of practical scenarios.Comment: 15 pages, 5 figure

Super-resolution generative adversarial networks of randomly-seeded fields

Reconstruction of field quantities from sparse measurements is a problem arising in a broad spectrum of applications. This task is particularly challenging when the mapping between sparse measurements and field quantities is performed in an unsupervised manner. Further complexity is added for moving sensors and/or random on–off status. Under such conditions, the most straightforward solution is to interpolate the scattered data onto a regular grid. However, the spatial resolution achieved with this approach is ultimately limited by the mean spacing between the sparse measurements. In this work, we propose a super-resolution generative adversarial network framework to estimate field quantities from random sparse sensors. The algorithm exploits random sampling to provide incomplete views of the high-resolution underlying distributions. It is hereby referred to as the randomly seeded super-resolution generative adversarial network (RaSeedGAN). The proposed technique is tested on synthetic databases of fluid flow simulations, ocean surface temperature distribution measurements and particle-image velocimetry data of a zero-pressure-gradient turbulent boundary layer. The results show excellent performance even in cases with high sparsity or noise level. This generative adversarial network algorithm provides full-field high-resolution estimation from randomly seeded fields with no need of full-field high-resolution representations for training.This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 949085) received by S.D. NOAA High Resolution SST data provided by the NOAA/OAR/ESRL PSL

Super-resolution Line Spectrum Estimation with Block Priors

We address the problem of super-resolution line spectrum estimation of an undersampled signal with block prior information. The component frequencies of the signal are assumed to take arbitrary continuous values in known frequency blocks. We formulate a general semidefinite program to recover these continuous-valued frequencies using theories of positive trigonometric polynomials. The proposed semidefinite program achieves super-resolution frequency recovery by taking advantage of known structures of frequency blocks. Numerical experiments show great performance enhancements using our method.Comment: 7 pages, double colum

Adaptive foveated single-pixel imaging with dynamic super-sampling

As an alternative to conventional multi-pixel cameras, single-pixel cameras enable images to be recorded using a single detector that measures the correlations between the scene and a set of patterns. However, to fully sample a scene in this way requires at least the same number of correlation measurements as there are pixels in the reconstructed image. Therefore single-pixel imaging systems typically exhibit low frame-rates. To mitigate this, a range of compressive sensing techniques have been developed which rely on a priori knowledge of the scene to reconstruct images from an under-sampled set of measurements. In this work we take a different approach and adopt a strategy inspired by the foveated vision systems found in the animal kingdom - a framework that exploits the spatio-temporal redundancy present in many dynamic scenes. In our single-pixel imaging system a high-resolution foveal region follows motion within the scene, but unlike a simple zoom, every frame delivers new spatial information from across the entire field-of-view. Using this approach we demonstrate a four-fold reduction in the time taken to record the detail of rapidly evolving features, whilst simultaneously accumulating detail of more slowly evolving regions over several consecutive frames. This tiered super-sampling technique enables the reconstruction of video streams in which both the resolution and the effective exposure-time spatially vary and adapt dynamically in response to the evolution of the scene. The methods described here can complement existing compressive sensing approaches and may be applied to enhance a variety of computational imagers that rely on sequential correlation measurements.Comment: 13 pages, 5 figure