Related papers: On the stability of some imaging functionals
Radiomics enables quantitative medical image analysis by converting imaging data into structured, high-dimensional feature representations for predictive modeling. Despite methodological developments and encouraging retrospective results,…
This paper investigates the possibility of improving radio interferometric images using an algorithm inspired by an optical method known as "lucky imaging", which would give more weight to the best-calibrated visibilities used to make a…
This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for…
Kinetic equations are often appropriate to model the energy density of high frequency waves propagating in highly heterogeneous media. The limitations of the kinetic model are quantified by the statistical instability of the wave energy…
We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for…
We present a comprehensive study of the resolution and stability properties of sparse promoting optimization theories applied to narrow band array imaging of localized scatterers. We consider homogeneous and heterogeneous media, and…
Radiomics is a promising technology that focuses on improvements of image analysis, using an automated high-throughput extraction of quantitative features. However, the character of lesion is affected by the surrounding tissue. A lesion on…
Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of…
This work presents a new super-resolution imaging approach by using subwavelength hole resonances. We employ a subwavelength structure in which an array of tiny holes are etched in a metallic slab with the neighboring distance $\ell$ that…
This contribution is a follow-up of a recent paper by the authors on adaptive, non-linear time-frequency transforms, focusing on the STFT based transforms. The adaptivity is provided by a focus function, that depends on the analyzed…
We study theoretically the spatial correlations between the intensities measured at the input and output planes of a disordered scattering medium. We show that at large optical thicknesses, a long-range spatial correlation persists and…
The problem considered here is the determination of the hamiltonian of a first quantized nonrelativistic particle by the help of some measurements of the location with a finite resolution. The resulting hamiltonian depends on the resolution…
The problem of optimization of propagation-based phase-contrast imaging setups is considered in the case of projection X-ray imaging and three-dimensional tomography with phase retrieval. For two-dimensional imaging, a simple model for a…
The dynamics of internal waves in stratified media, such as the ocean or atmosphere, is highly dependent on the topography of their floor. A closed-form analytical solution can be derived only in cases when the water distribution density…
Medical imaging quantitative features had once disputable usefulness in clinical studies. Nowadays, advancements in analysis techniques, for instance through machine learning, have enabled quantitative features to be progressively useful in…
In this paper we give a first attempt to define and study stable distributions with respect to the weak generalized convolution, focusing our attention on the symmetric weakly stable distribution. As in the case of the classical…
In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a…