Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

We consider the restoration of piecewise constant images where the number of the regions and their values are not fixed in advance, with a good difference of piecewise constant values between neighboring regions, from noisy data obtained at the output of a linear operator (e.g., a blurring kernel or a Radon transform). Thus we also address the generic problem of unsupervised segmentation in the context of linear inverse problems. The segmentation and the restoration tasks are solved jointly by minimizing an objective function (an energy) composed of a quadratic data-fidelity term and a nonsmooth nonconvex regularization term. The pertinence of such an energy is ensured by the analytical properties of its minimizers. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonsmooth nonconvex minimization. Indeed, the existing methods are unsatisfactory since they (implicitly or explicitly) involve a smooth approximation of the regularization term and often get stuck in shallow local minima. The goal of this paper is to design a method that efficiently handles the nonsmooth nonconvex minimization. More precisely, we propose a continuation method where one tracks the minimizers along a sequence of approximate nonsmooth energies {Jε}, the first of which being strictly convex and the last one the original energy to minimize. Knowing the importance of the nonsmoothness of the regularization term for the segmentation task, each Jε is nonsmooth and is expressed as the sum of an l1 regularization term and a smooth nonconvex function. Furthermore, the local minimization of each Jε is reformulated as the minimization of a smooth function subject to a set of linear constraints. The latter problem is solved by the modified primal-dual interior point method, which guarantees the descent direction at each step. Experimental results are presented and show the effectiveness and the efficiency of the proposed method. Comparison with simulated annealing methods further shows the advantage of our method.published_or_final_versio

COMPARISON OF DENOISING FILTERS ON COLOUR TEM IMAGE FOR DIFFERENT NOISE

TEM (Transmission Electron Microscopy) is an important morphological characterization tool for Nanomaterials. Quite often a microscopy image gets corrupted by noise, which may arise in the process of acquiring the image, or during its transmission, or even during reproduction of the image. Removal of noise from an image is one of the most important tasks in image processing. Denoising techniques aim at reducing the statistical perturbations and recovering as well as possible the true underlying signal. Depending on the nature of the noise, such as additive or multiplicative type of noise, there are several approaches towards removing noise from an image. Image De-noising improves the quality of images acquired by optical, electro-optical or electronic microscopy. This paper compares five filters on the measures of mean of image, signal to noise ratio, peak signal to noise ratio & mean square error. In this paper four types of noise (Gaussian noise, Salt & Pepper noise, Speckle noise and Poisson noise) is used and image de-noising performed for different noise by various filters (WFDWT, BF, HMDF, FDE, DVROFT). Further results have been compared for all noises. It is observed that for Gaussian Noise WFDWT & for other noises HMDF has shown the better performance results

Thermal imaging in the 3-5 micron range for precise localization of defects: Application on frescoes at the Sforza Castle

Infrared methods are of great importance in nondestructive testing of artworks, allowing a remote and wide-field imaging of interesting hidden features. Here we discuss a workflow based on thermal imaging in the mid infrared 3-5 micron range for the evaluation of subsurface defects in frescoes. Particular attention is payed to obtaining a high resolution (submillimetric) localization of the defects. The transfer of diagnostics techniques into real world applications, is discussed through the proof of concept of the proposed workflow on frescoes at the Sforza Castle (Milan, Italy)

Real-time study of transients during high-temperature creep of an Ni-base superalloy by far-field high-energy synchrotron X-ray diffraction

The high-temperature mechanical behavior of single-crystal Ni-base superalloys has been formerly studied by in situ triple-crystal synchrotron X-ray diffractometry (TCD). However, the 1/300 s recording frequency does not allow real-time tests. It is shown here that real-time monitoring is possible with far-field diffractometry in transmission. The use of a far-field camera enables one to follow a diffraction spot with high angular precision and high recording speed. This technique allows measurement of the mechanical response of an AM1 Nibase single-crystal superalloy following steep load jumps and relaxations during high-temperature creep tests. Local crystal misorientation is revealed and rafting (oriented coalescence) is examined. This new technique is compared with TCD, in order to highlight its benefits and drawbacks

SNR Spectra as a Quantitative Model for Image Quality in Polychromatic X-Ray Imaging

In polychromatic x-ray imaging for nondestructive testing, material science or medical applications, image quality is usually a problem of detecting sample structure in noisy data. This problem is typically stated this way: As many photons as possible need to be detected to get a good image quality. We instead propose to use the concept of signal detection, which is more universal. In signal detection, it is the sample properties which are detected. Photons play the role of information carriers for the signal. Signal detection for example allows modeling the effects which polychromaticity has on image quality. $\mathit{SNR}$ spectra (= spatial $\mathit{SNR}$) are used as a quantity to describe if reliable signal detection is possible. They include modulation transfer and phase contrast in addition to noisiness effects. $\mathit{SNR}$ spectra can also be directly measured, which means that theoretical predictions can easily be tested. We investigate the effects of signal and noise superposition on the $\mathit{SNR}$ spectrum and show how selectively not detecting photons can increase the image quality

Imaging shape and strain in nanoscale engineered semiconductors for photonics by coherent x-ray diffraction

Coherent x-ray diffractive imaging is a nondestructive technique that extracts three-dimensional electron density and strain maps from materials with nanometer resolution. It has been utilized for materials in a range of applications, and has significant potential for imaging buried nanostructures in functional devices. Here, we show that coherent x-ray diffractive imaging is able to bring new understanding to a lithography-based nanofabrication process for engineering the optical properties of semiconducting GaAs1-yNy on a GaAs substrate. This technique allows us to test the process reliability and the manufactured patterns quality. We demonstrate that regular and sharp geometrical structures can be produced on a few-micron scale, and that the strain distribution is uniform even for highly strained sub-microscopic objects. This nondestructive study would not be possible using conventional microscopy techniques. Our results pave the way for tailoring the optical properties of emitters with nanometric precision for nanophotonics and quantum technology applications

High resolution laboratory x-ray tomography for biomedical research : From design to application

Laboratory x-ray micro- and nano-tomography are emerging techniques in biomedical research. Through the use of phase-contrast, sufficient contrast can be achieved in soft tissue to support medical studies. With ongoing developments of x-ray sources and detectors, biomedical studies can increasingly be performed at the laboratory and do not necessary require synchrotron radiation. Particularly nano-focus x-ray sources offer new possibilities for the study of soft tissue. However, with increasing resolution, the complexity and stability requirements on laboratory systems advance as well. This thesis describes the design and implementation of two systems: a micro- CT and a nano-CT, which are used for biomedical imaging.To increase the resolution of the micro-CT, super-resolution imaging is adopted and evaluated for x-ray ima- ging, grating-based imaging and computed tomography utilising electromagnetic stepping of the x-ray source to acquire shifted low-resolution images to estimate a high-resolution image. The experiments have shown that super-resolution can significantly improve the resolution in 2D and 3D imaging, but also that upscaling during the reconstruction can be a viable approach in tomography, which does not require additional images.Element-specific information can be obtained by using photon counting detectors with energy-discriminating thresholds. By performing a material decomposition, a dataset can be split into multiple different materials. Tissue contains a variety of elements with absorption edges in the range of 4 – 11 keV, which can be identified by placing energy thresholds just below and above these edges, as we have demonstrated using human atherosclerotic plaques.An evaluation of radiopaque dyes as alternative contrast agent to identify vessels in lung tissue was performed using phase contrast micro-tomography. We showed that the dye solutions have a sufficiently low density to not cause any artefacts while still being able to separate them from the tissue and distinguish them from each other.Finally, the design and implementation of the nano-CT system is discussed. The system performance is assessed in 2D and 3D, achieving sub-micron resolution and satisfactory tissue contrast through phase contrast. Applica- tion examples are presented using lung tissue, a mouse heart, and freeze dried leaves