Because the refractive index for hard x rays is slightly different from unity, the optical phase of a beam is affected by transmission through an object. Phase images can be obtained with extreme instrumental simplicity by simple propagation provided the beam is coherent. But, unlike absorption, the phase is not simply related to image brightness. A holographic reconstruction procedure combining images taken at different distances from the specimen was developed. It results in quantitative phase mapping and, through association with three-dimensional reconstruction, in holotomography, the complete three-dimensional mapping of the density in a sample. This tool in the characterization of materials at the micrometer scale is uniquely suited to samples with low absorption contrast and radiation-sensitive systems.

The problem of parameter estimation from Rician distributed data (e.g., magnitude magnetic resonance images) is addressed. The properties of conventional estimation methods are discussed and compared to maximum-likelihood (ML) estimation which is known to yield optimal results asymptotically. In contrast to previously proposed methods, ML estimation is demonstrated to be unbiased for high signal-to-noise ratio (SNR) and to yield physical relevant results for low SNR.

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The use of a coherent field-emission electron source in transmission electron microscopy is combined with phase retrieval by digital processing of a focal image series. For the first time, a dramatic improvement of the high-resolution performance of the electron microscope beyond the usual "point-to-point" resolution has been realized: Experiments on a 200-kV microscope with a point resolution of 0.24 nm reveal reconstructed information down to 0.14 nm. Examples are shown in the field of high-Tc superconductors and ferroelectric oxides. The oxygen sublattice in these structures is revealed.

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We conjecture that texture can be characterized by the statistics of the wavelet detail coefficients and therefore introduce two feature sets: (1) the wavelet histogram signatures which capture all first order statistics using a model based approach and (2) the wavelet co-occurrence signatures, which reflect the coefficients' second-order statistics. The introduced feature sets outperform the traditionally used energy. Best performance is achieved by combining histogram and co-occurrence signatures.

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