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We propose a new gradient projection algorithm that compares favorably with the fastest algorithms available to date for {$\ell_1$}-constrained sparse recovery from noisy data, both in the compressed sensing and inverse problem frameworks. The method exploits a line-search along the feasible direction and an adaptive steplength selection based on recent strategies for the alternation of the well-known Barzilai-Borwein rules. The convergence of the proposed approach is discussed and a computational study on both well-conditioned and ill-conditioned problems is carried out for performance evaluations in comparison with five other algorithms proposed in the literature., SCOPUS: le.j, info:eu-repo/semantics/published

info:eu-repo/semantics/published

Fredholm integral equations of the first kind are the mathematical model common to several electromagnetic, optical and acoustical inverse scattering problems. In most of these problems the solution must be positive in order to satisfy physical plausibility. We consider ill-posed deconvolution problems and investigate several linear regularization algorithms which provide positive approximate solutions at least in the absence of errors on the data., info:eu-repo/semantics/published

info:eu-repo/semantics/published

Previous work in this series, in which the theory of singular systems has been used to discuss the problem of diffraction-limited imaging, is generalized to allow the reconstruction of an object over a region with ‘soft’ edges. The generalization is introduced to deal with gaussian-beam or other illumination or uncertain a priori knowledge of position. The solutions are developed in a weighted L2 space. Examples of singular functions and vectors with both gaussian and sine illumination are given. The analysis is applied to determine the amplitude response functions of the scanning optical or acoustic microscope systems proposed by Bertero and Pike in the first paper of the series and it is found that the performance of a scanning microscope of the new type should approach exactly that of a conventional coherent microscope of twice the resolving power. © 1984 Taylor & Francis Group, LLC., SCOPUS: ar.j, info:eu-repo/semantics/published

info:eu-repo/semantics/published

info:eu-repo/semantics/published

info:eu-repo/semantics/published

In 1982 Bertero and Pike [1] showed that superresolution was possible in microscopy by recording the image over a larger area than the geometric one and subsequent inversion of the data by, for example, a singular system analysis. In a series of papers following, these authors and others have considered a number of special cases, both analytically and numerically. In this paper we investigate the incoherent case, which applies to confocal scanning fluorescence microscopy, in 1-D. Numerical studies have already given a clear indication of the form of the results for the case of an infinite recorded image, indicating a transfer function of the curious form shown in figure 1.

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., info:eu-repo/semantics/published

info:eu-repo/semantics/published

info:eu-repo/semantics/published

info:eu-repo/semantics/published

info:eu-repo/semantics/published