Forecast verification is a crucial task for assessing the predictive power of prognostic model forecasts and it is usually implemented by checking quality-based skill scores. In this article, we propose a novel approach to realize forecast verification focusing not just on the forecast quality but rather on its value. Specifically, we introduce a strategy for assessing the severity of forecast errors based on the evidence that, on the one hand, a false alarm just anticipating an occurring event is better than one in the middle of consecutive nonoccurring events, and that, on the other hand, a miss of an isolated event has a worse impact than a miss of a single event, which is part of several consecutive occurrences. Relying on this idea, we introduce a notion of value-weighted skill scores giving greater importance to the value of the prediction rather than to its quality. Then, we introduce an ensemble strategy to maximize quality-based and value-weighted skill scores independently of one another. We test it on the predictions provided by deep learning methods for binary classification in the case of four applications concerned with pollution, space weather, stock price, and IoT data stream forecasting. Our experimental studies show that using the ensemble strategy for maximizing the value-weighted skill scores generally improves both the value and quality of the forecast.

Although characterized by two different mathematical definitions, both the Radon and the Hough transforms ultimately take an image as input and provide, as output, functions defined on a preassigned parameter space, i.e., the so-called Radon and Hough sinograms, respectively. The parameters in these two spaces describe a family of curves, which represent either the integration domains considered in the Radon transform, or the kind of curves to be detected by the Hough transform. It is heuristically known that the Hough sinogram converges to the corresponding Radon sinogram when the discretization step in the parameter space tends to zero. However, as far as we know, no formal result has been proven so far about such convergence. Therefore, by considering generalized functions in a multidimensional setting, in this paper we give an analytical proof of this heuristic rationale when the input digital image is described as a set of grayscale points, that is, as a sum of weighted Dirac delta functions. On these grounds, we also show that this asymptotic equivalence may lead to a visualization process relying on the interpretation of the Radon sinogram as a Hough sinogram.

Parametric imaging of nuclear medicine data exploits dynamic functional images in order to reconstruct maps of kinetic parameters related to the metabolism of a specific tracer injected in the biological tissue. Classical approaches to parametric imaging rely on linearized schemes that, on the one hand, are computationally effective but, on the other hand, provide information just on a very limited number of parameters (typically two). Possible nonlinearized approaches require the pixelwise numerical solution of compartmental nonlinear ill-posed inverse problems and therefore typically imply a notable computational burden. In the present paper we introduce a fast numerical optimization scheme for parametric imaging relying on a regularized version of the standard affine-scaling trust-region method. The main advantages of this approach are both that it is a regularization method (and therefore it reduces the numerical instabilities in the reconstructed images) and that it is significantly faster than other algorithms in the optimization market (and therefore it may be utilized for clinical applications). The validation of this approach is realized in a simulation framework for brain imaging and also in the case of an experimental set of nuclear medicine data acquired from a murine model. Comparison of performances is made with respect to a regularized Gauss--Newton scheme and a standard nonlinear bound-constrained least-squares algorithm.

The Spectrometer/Telescope for Imaging X-rays (STIX) is a hard X-ray imaging spectroscopy device to be mounted in the Solar Orbiter cluster with the aim of providing images and spectra of solar flaring regions at different photon energies in the range from a few keV to around 150 keV. The imaging modality of this telescope is based on the Moiré pattern concept and utilizes 30 subcollimators, each one containing a pair of co-axial grids. This paper applies Fourier analysis to provide the first rigorous description of the data formation process in STIX. Specifically, we show that, under the fundamental frequency approximation, the integrated counts measured by STIX subcollimators can be interpreted as specific spatial Fourier components of the incoming photon flux, named visibilities. Fourier analysis also allows the quantitative assessment of the reliability of such interpretation. The description of STIX data in terms of visibilities has a notable impact on the image reconstruction process, since it fosters the application of Fourier-based imaging algorithms.

The Hough transform is a standard pattern recognition technique introduced between the 1960s and the 1970s for the detection of straight lines, circles, and ellipses. Here we offer a mathematical foundation, based on algebraic-geometry arguments, of an extension of this approach to the automated recognition of rational cubic, quartic, and elliptic curves. The accuracy of this approach is tested against synthetic data and in the case of experimental observations provided by the NASA Solar Dynamics Observatory mission.

We develop a formal procedure for the analysis of imaging spectroscopy data, i.e., remote sensing observations of the structure of a radiation source as a function of an observed parameter (e.g., radiation wavelength, frequency, or energy) and two-dimensional location in the observation plane of the instrument used. In general, imaging spectroscopy involves inversions of both spatial and spectral information. “Traditional” approaches typically proceed by performing the spatial inversion first, and then applying spectral deconvolution algorithms on a “pixel-by-pixel” basis across the source to deduce the (line-of-sight-weighted) form of the “source function” (a function involving only physical properties of the source itself) at each location in the observation plane. However, in the special case where spatial information is encoded in the form of visibilities (two-dimensional spatial Fourier transforms of the source structure), it is advantageous, both conceptually and computationally, to reverse the order of the steps in this procedure. In such an alternative approach, the spectral inversion is performed first, yielding visibilities of the unknown source function, and then these source function visibilities are spatially transformed to yield in situ information on the source, as a function of both energy and position. We illustrate the power and fidelity of this method using simulated data and apply it to hard X-ray observations of a solar flare on April 15, 2002. We also discuss briefly its broader applicability.

In this letter, we investigate the impact of choosing different loss functions from the viewpoint of statistical learning theory. We introduce a convexity assumption, which is met by all loss functions commonly used in the literature, and study how the bound on the estimation error changes with the loss. We also derive a general result on the minimizer of the expected risk for a convex loss function in the case of classification. The main outcome of our analysis is that for classification, the hinge loss appears to be the loss of choice. Other things being equal, the hinge loss leads to a convergence rate practically indistinguishable from the logistic loss rate and much better than the square loss rate. Furthermore, if the hypothesis space is sufficiently rich, the bounds obtained for the hinge loss are not loosened by the thresholding stage.

Chirp-pulse microwave computerized tomography (CP-MCT) is an imaging modality developed at the Department of Biocybernetics, University of Niigata (Niigata, Japan), which intends to reduce the microwave-tomography problem to an X-ray-like situation. We have recently shown that data acquisition in CP-MCT can be described in terms of a linear model derived from scattering theory. In this paper, we validate this model by showing that the theoretically computed response function is in good agreement with the one obtained from a regularized multiple deconvolution of three data sets measured with the prototype of CP-MCT. Furthermore, the reliability of the model as far as image restoration in concerned, is tested in the case of space-invariant conditions by considering the reconstruction of simple on-axis cylindrical phantoms.