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Estimating the absolute orientation of a local system relative to a global navigation satellite system (GNSS) reference often suffers from local minima and high dependency on satellite availability. Existing methods for this alignment task…
In this paper I present three new results of astronomical interest concerning the theory of Abel inversion. 1) I show that in the case of a spatial emissivity that is constant on toroidal surfaces and projected along the symmetry axis…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
Millimeter wave radar can measure distances, directions, and Doppler velocity for objects in harsh conditions such as fog. The 4D imaging radar with both vertical and horizontal data resembling an image can also measure objects' height.…
We discuss the implementation of Bayesian inversion methods in order to recover the properties of the intergalactic medium from observations of the neutral hydrogen Lyman-$\alpha$ absorptions observed in the spectra of high redshift quasars…
Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \mid y)$. While posterior sampling is valuable for capturing uncertainty and multi-modality, many classical and practical…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
Creating plausible surfaces is an essential component in achieving a high degree of realism in rendering. To relieve artists, who create these surfaces in a time-consuming, manual process, automated retrieval of the spatially-varying…
The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…
Hyperspectral imaging is a cutting-edge type of remote sensing used for mapping vegetation properties, rock minerals and other materials. A major drawback of hyperspectral imaging devices is their intrinsic low spatial resolution. In this…
Imaging in thick biological tissues is often degraded by sample-induced aberrations, which reduce image quality and resolution, particularly in super-resolution techniques. While hardware-based adaptive optics, which correct aberrations…
Flux calibration of spectra in reverberation mapping (RM) is most often performed by assuming the flux constancy of some specified narrow emission lines, which stem from an extended region that is sometimes partially spatially resolved, in…
In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…
Reliable odometry is essential for mobile robots as they increasingly enter more challenging environments, which often contain little information to constrain point cloud registration, resulting in degraded LiDAR-Inertial Odometry (LIO)…
Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high-resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often…
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…
Depth imaging is a crucial area in Autonomous Driving Systems (ADS), as it plays a key role in detecting and measuring objects in the vehicle's surroundings. However, a significant challenge in this domain arises from missing information in…
Intrinsic imaging or intrinsic image decomposition has traditionally been described as the problem of decomposing an image into two layers: a reflectance, the albedo invariant color of the material; and a shading, produced by the…
An expression is obtained on the basis of phase perturbation theory for the contribution to the mean differential reflection coefficient from the in-plane co-polarized component of the light scattered diffusely from a two-dimensional…