Numerical methods for linear least squaresNumerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).
Time–frequency analysisIn signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform.
Phase retrievalPhase retrieval is the process of algorithmically finding solutions to the phase problem. Given a complex signal , of amplitude , and phase : where x is an M-dimensional spatial coordinate and k is an M-dimensional spatial frequency coordinate. Phase retrieval consists of finding the phase that satisfies a set of constraints for a measured amplitude. Important applications of phase retrieval include X-ray crystallography, transmission electron microscopy and coherent diffractive imaging, for which .
Interferometric visibilityThe interferometric visibility (also known as interference visibility and fringe visibility, or just visibility when in context) is a measure of the contrast of interference in any system subject to wave superposition. Examples include as optics, quantum mechanics, water waves, sound waves, or electrical signals. Visibility is defined as the ratio of the amplitude of the interference pattern to the sum of the powers of the individual waves. The interferometric visibility gives a practical way to measure the coherence of two waves (or one wave with itself).
Solutions fondées sur la natureLes solutions fondées sur la nature (ou SFN, en anglais nature-based solutions, NBS) font référence à la gestion et à l'utilisation durables de la nature pour relever les défis socio-environnementaux. Ces défis incluent des questions telles que le changement climatique, la sécurité de l'eau, la pollution de l'eau, la sécurité alimentaire, la santé humaine, la perte de biodiversité et la gestion des risques de catastrophes.
Fentes de YoungLes fentes de Young (ou interférences de Young) désignent en physique une expérience qui consiste à faire interférer deux faisceaux de lumière issus d'une même source, en les faisant passer par deux petits trous percés dans un plan opaque. Cette expérience fut réalisée pour la première fois par Thomas Young en 1801 et permit de comprendre le comportement et la nature de la lumière. Sur un écran disposé en face des fentes de Young, on observe un motif de diffraction qui est une zone où s'alternent des franges sombres et illuminées.
