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We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate…
This paper introduces an elasticity reconstruction method based on local displacement observations of elastic bodies. Sparse reconstruction theory is applied to formulate the underdetermined inverse problems of elasticity reconstruction…
X-ray ptychography is one of the versatile techniques for nanometer resolution imaging. The magnitude of the diffraction patterns is recorded on a detector and the phase of the diffraction patterns is estimated using phase retrieval…
The question whether one can recover the shape of a geometric object from its Laplacian spectrum ('hear the shape of the drum') is a classical problem in spectral geometry with a broad range of implications and applications. While…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Diffractive lenses have recently been applied to the domain of multispectral imaging in the X-ray and UV regimes where they can achieve very high resolution as compared to reflective and refractive optics. Conventionally, spectral…
Imaging below the diffraction limit is always a public interest because of the restricted resolution of conventional imaging systems. To beat the limit, evanescent harmonics decaying in space must participate in the imaging process. Here,…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
In a recent paper (Brown & Battye 2011), we proposed the use of integrated polarization measurements of background galaxies in radio weak gravitational lensing surveys and investigated the potential impact on the statistical measurement of…
Rescattering electrons offer great potential as probes of molecular properties on ultrafast timescales. The most famous example is molecular tomography, in which high harmonic spectra of oriented molecules are mapped to ``tomographic…
We consider the scattering of time-harmonic plane waves by a compactly supported inhomogeneous scattering obstacle governed by the Helmholtz equation. Given far field observations of the scattered fields corresponding to plane wave incident…
We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…
We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…
On-chip spectral imaging based on engineered spectral modulation and computational spectral reconstruction provides a promising scheme for portable spectral cameras. However, the angle dependence of modulation units results in the angle…
This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as…
In this paper we consider the reconstruction problem of photoacoustic tomography (PAT) with a flat observation surface. We develop a direct reconstruction method that employs regularization with wavelet sparsity constraints. To that end, we…
This work presents new methods and algorithms for tracking the shape and trajectory of moving reflecting obstacles with broken rays, or rays reflecting at an obstacle. While in tomography the focus of the reconstruction method is to recover…