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.

Object Restoration Beyond the Rayleigh Limit in the Presence of Noise

info:eu-repo/semantics/published

Measurements and simulations of noise imposed on supercontinuum generated in microstructure fiber

We present experimental and theoretical investigations of the highly nonlinear and broadband noise that exists on supercontinuum spectra generated from launching femtosecond Ti:Sapphire pulses into microstructure fiber.

Amplitude noise on supercontinuum generated in microstructure fiber: Measurements and simulations

Supercontinua generated in microstructure fiber can exhibit significant excess amplitude noise. We present experimental and numerical studies of the origins of this excess noise and its dependence on the input laser pulse parameters.

Fundamental Amplitude Noise Limitations to Supercontinuum Spectra Generated in a Microstructured Fiber

Broadband supercontinuum spectra are generated in a microstructured fiber using femtosecond laser pulses. Noise properties of these spectra are studied through experiments and numerical simulations based on a generalized stochastic nonlinear Schrödinger equation. In particular, the relative intensity noise as a function of wavelength across the supercontinuum is measured over a wide range of input pulse parameters, and experimental results and simulations are shown to be in good quantitative agreement. For certain input pulse parameters, amplitude fluctuations as large as 50% are observed. The simulations clarify that the intensity noise on the supercontinuum arises from the amplification of two noise inputs during propagation - quantum-limited shot noise on the input pulse, and spontaneous Raman scattering in the fiber. The amplification factor is a sensitive function of the input pulse parameters. Short input pulses are critical for the generation of very broad supercontinua with low noise.

Fundamental Amplitude Noise Limitations to Supercontinuum Spectra Generated in a Microstructured Fiber: Erratum

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Erratum: Fundamental amplitude noise limitations to supercontinuum spectra generated in a microstructured fiber (Appl. Phys. B (2003) 77 (269-277))

SCOPUS: er.j

Fundamental Noise Limitations to Supercontinuum Generation in Microstructure Fiber

Broadband noise on supercontinuum spectra generated in microstructure fiber is shown to lead to amplitude fluctuations as large as 50% for certain input laser pulse parameters. We study this noise using both experimental measurements and numerical simulations with a generalized stochastic nonlinear Schrödinger equation, finding good quantitative agreement over a range of input-pulse energies and chirp values. This noise is shown to arise from nonlinear amplification of two quantum noise inputs: the input-pulse shot noise and the spontaneous Raman scattering down the fiber.