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An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…
An image or volume of interest in positron emission tomography (PET) is reconstructed from pairs of gamma rays emitted from a radioactive substance. Many image reconstruction methods are based on estimation of pixels or voxels on some…
An important goal in molecular physics and chemistry today is to obtain structure-dependent information about molecular function to obtain a deeper understanding into chemical reactions. However, until now, asymmetric tops, which comprise…
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…
Recently, a method to image molecular electronic wave functions using high harmonic generation (HHG) was introduced by Itatani \textit{et al.\} [Nature {\textbf{432}}, 876 (2004)]. We show that, while the tomographic reconstruction of…
Characterizing the phase space distribution of particle beams in accelerators is a central part of accelerator understanding and performance optimization. However, conventional reconstruction-based techniques either use simplifying…
The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In…
Spectral domain optical coherence tomography (OCT) offers high resolution multidimensional imaging, but generally suffers from defocussing, intensity falloff and shot noise, causing artifacts and image degradation along the imaging depth.…
Electrical impedance tomography is an imaging modality for extracting information on the conductivity distribution inside a physical body from boundary measurements of current and voltage. In many practical applications, it is a priori…
The application of a matrix-based reconstruction protocol for obtaining Molecular Frame (MF) photoelectron angular distributions (MFPADs) from laboratory frame (LF) measurements (LFPADs) is explored. Similarly to other recent works on the…
Speckle Imaging based on triple correlation is a very efficient image reconstruction technique which is used to retrieve Fourier phase information of the object in presence of atmospheric turbulence. We have developed both Direct Bispectrum…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
The ability to directly follow and time resolve the rearrangement of the nuclei within molecules is a frontier of science that requires atomic spatial and few-femtosecond temporal resolutions. While laser induced electron diffraction can…
A new algorithmic framework is presented for holographic phase retrieval via maximum likelihood optimization, which allows for practical and robust image reconstruction. This framework is especially well-suited for holographic coherent…
An iterative algorithm for reconstructing the photon distribution from the random phase homodyne statistics is discussed. This method, derived from the maximum-likelihood approach, yields a positive definite estimate for the photon…
Reconstruction of in-line holograms of unknown objects in general suffers from twin-image artifacts due to the appearance of an out-of-focus image overlapping with the desired image to be reconstructed. Computer-based iterative phase…
High-order harmonic generation is a powerful and sensitive tool for probing atomic and molecular structures, combining in the same measurement an unprecedented attosecond temporal resolution with a high spatial resolution, of the order of…
Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free…
We theoretically demonstrate a scheme for tomographic reconstruction of asymmetric molecular orbitals based on high-order harmonic generation with a two-color multicycle laser field. It is shown that by adjusting the relative phase of the…