Regularized iterative and noniterative procedures for object restoration in the presence of noise :an error analysis

An analysis is carried out, using the prolate spheroidal wave functions, of certain regularized iterative and noniterative methods previously proposed for the achievement of object restoration (or, equivalently, spectral extrapolation) from noisy image data. The ill-posedness inherent in the problem is treated by means of a regularization parameter, and the analysis shows explicitly how the deleterious effects of the noise are then contained. The error in the object estimate is also assessed, and it is shown that the optimal choice for the regularization parameter depends on the signal-to-noise ratio. Numerical examples are used to demonstrate the performance of both unregularized and regularized procedures and also to show how, in the unregularized case, artefacts can be generated from pure noise. Finally, the relative error in the estimate is calculated as a function of the degree of superresolution demanded for reconstruction problems characterized by low space–bandwidth products.

Super-resolution in confocal scanning microscopy: II :The incoherent case

For pt.I see ibid. vol.3, p.195 (1987). The authors have shown that the resolution of a confocal scanning microscope can be improved by recording the full image at each scanning point and then inverting the data. These analyses were restricted to the case of coherent illumination. They investigate, along similar lines, the incoherent case, which applies to fluorescence microscopy. They investigate the one-dimensional and two-dimensional square-pupil problems and they prove, by means of numerical computations of the singular value spectrum and of the impulse response function, that for a signal-to-noise ratio of, say 10%, it is possible to obtain an improvement of approximately 60% in resolution with respect to the conventional incoherent light confocal microscope. This represents a working bandwidth of 3.5 times the Rayleigh limit.