Resolution beyond the diffraction limit for regularized object restoration

We propose a new formulation of Miller's regularization theory, which is particularly suitable for object restoration problems. By means of simple geometrical arguments, we obtain upper and lower bounds for the errors on regularized solutions. This leads to distinguish between ' Holder continuity ' which is quite good for practical computations and ` logarithmic continuity ' which is very poor. However, in the latter case, one can reconstruct local weighted averages of the solution. This procedure allows for precise valuations of the resolution attainable in a given problem. Numerical computations, made for object restoration beyond the diffraction limit in Fourier optics, show that, when logarithmic continuity holds, the resolution is practically independent of the data noise level. © 1980 Taylor & Francis Group, LLC.

Number of degrees of freedom in inverse diffraction

The problem of inverse diffraction from plane to plane is considered in the case where a finite aperture exists in the boundary plane. Singular values and singular functions for the problem are introduced, and the number of degrees of freedom is defined in terms of the distribution of the singular values. Numerical computations are presented for the one-dimensional problem, and it is shown that the effect of evanescent waves disappears at a distance of approximately one wavelength from the boundary plane, even when the dimension of the slit is comparable with the wavelength of the diffracted field. © 1983 Taylor & Francis Group, LLC.

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.

Resources, experience and perseverance in entrepreneurs' perceived likelihood of success in an emerging economy

This paper introduces new results obtained from a statistical investigation into a 3071-observation data set collected from a Vietnamese nationwide entrepreneurship survey. From established relationships, such factors as preparedness, financial resources and participation in social networks are confirmed to have significant effects on entrepreneurial decisions. Entrepreneurs, both financially constrained and unconstrained, who have a business plan tend to start their entrepreneurial ventures earlier. Also, financial constraints have a profound impact on the entrepreneurial decisions. When perceiving the likelihood of success to be high, an entrepreneur shows the tendency for prompt action on business ideas. But when seeing the risk of prolonging the waiting time to first revenue, a prospective entrepreneur would be more likely to wait for more favorable conditions despite the vagueness of "favorable". Additionally, empirical computations indicate that there is a 41.3% probability that an extant entrepreneur who is generating revenue sees high chance of success. Past work and entrepreneurial experiences also have positive impacts on both the entrepreneurial decisions and perceived chance of success.