Super-resolution in confocal scanning microscopy: generalized inversion formulae

It was shown in previous papers that the resolution of a confocal scanning microscope can be significantly improved by measuring, for each scanning position, the full diffraction image and by inverting these data to recover the value of the object at the confocal point. In the present work, the authors generalize the data inversion procedure by allowing, for reconstructing the object at a given point, to make use of the data samples recorded at other scanning positions. This leads them to a family of generalized inversion formulae, either exact or approximate. Some previously known formulae are re-derived here as special cases in a particularly simple way.

Inversion from redundant data

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Resolution enhancement by data inversion techniques

Chapter 15

Iterative inversion of experimental data in weighted spaces

We present iterative algorithms for solving linear inverse problems with discrete data and compare their performances with the method of singular function expansion, in view of applications in optical imaging and particle sizing.

Inversion of light scattering data by singular system analysis

We consider the problem of inverting experimental data obtained in light scattering experiments described by linear theories. We discuss applications to particle sizing and we describe fast and easy-to-implement algorithms which permit the extraction, from noisy measurements, of reliable information about the particle size distribution. © 1987, SPIE.

The Use of Singular Systems and other Inversion Methods in Weighted L2- spaces

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Particle sizing by inversion of extinction data

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A new inversion procedure for confocal scanning microscopy and other bandlimited signal processing problems

We find a simple analytic expression for the inverse of an infinite matrix related to the problem of data reduction in confocal scanning microscopy and other band-limited signal processing problems. Potential applications of this result to practical problems are outlined. The matrix arises from a sampling expansion approach to the integral equation.

Generalized ocean color inversion model for retrieving marine inherent optical properties

Ocean color measured from satellites provides daily, global estimates of marine inherent optical properties (IOPs). Semi-analytical algorithms (SAAs) provide one mechanism for inverting the color of the water observed by the satellite into IOPs. While numerous SAAs exist, most are similarly constructed and few are appropriately parameterized for all water masses for all seasons. To initiate community-wide discussion of these limitations, NASA organized two workshops that deconstructed SAAs to identify similarities and uniqueness and to progress toward consensus on a unified SAA. This effort resulted in the development of the generalized IOP (GIOP) model software that allows for the construction of different SAAs at runtime by selection from an assortment of model parameterizations. As such, GIOP permits isolation and evaluation of specific modeling assumptions, construction of SAAs, development of regionally tuned SAAs, and execution of ensemble inversion modeling. Working groups associated with the workshops proposed a preliminary default configuration for GIOP (GIOP-DC), with alternative model parameterizations and features defined for subsequent evaluation. In this paper, we: (1) describe the theoretical basis of GIOP; (2) present GIOP-DC and verify its comparable performance to other popular SAAs using both in situ and synthetic data sets; and, (3) quantify the sensitivities of their output to their parameterization. We use the latter to develop a hierarchical sensitivity of SAAs to various model parameterizations, to identify components of SAAs that merit focus in future research, and to provide material for discussion on algorithm uncertainties and future emsemble applications.

MSGR-based Low Latency Complex Matrix Inversion Architecture

This paper presents a matrix inversion architecture based on the novel Modified Squared Givens Rotations (MSGR) algorithm, which extends the original SGR method to complex valued data, and also corrects erroneous results in the original SGR method when zeros occur on the diagonal of the matrix either initially or during processing. The MSGR algorithm also avoids complex dividers in the matrix inversion, thus minimising the complexity of potential real-time implementations. A systolic array architecture is implemented and FPGA synthesis results indicate a high-throughput low-latency complex matrix inversion solution. © 2008 IEEE.