Related papers: Error Correction for Discrete Tomography
We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…
This paper presents a novel Direct Integration Theorem (DIT), derived as a non-trivial corollary of the classical Central Slice Theorem (CST). The DIT provides a mathematically consistent transition from the continuous to the discrete…
In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a…
Much recent progress has been made in reconstructing the 3D shape of an object from an image of it, i.e. single view 3D reconstruction. However, it has been suggested that current methods simply adopt a "nearest-neighbor" strategy, instead…
While Diffusion Language Models (DLMs) are theoretically well-suited for iterative refinement due to their non-causal structure, they often fail to reliably revise incorrect tokens in practice. The key challenge lies in the model's…
The Diffuse Optical Tomography (DOT) has received considerable attention in the recent years in the field of biomedical imaging and disease detection. However, imaging through highly diffusive medium is a challenge and stability is always…
Optoacoustic tomography image reconstruction has been a problem of interest in recent years. By exploiting the exceptional generative power of the recently proposed diffusion models we consider a scheme which is based on a conditional…
In this paper we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II for reconstructing the input vector $\mathbf x\in\mathbb R^N$, $N=2^J$, with short support of length $m$ from its discrete…
Boundary detection of irregular and translucent objects is an important problem with applications in medical imaging, environmental monitoring and manufacturing, where many of these applications are plagued with scarce labeled data and low…
Conformal defects spontaneously break part of the symmetry algebra of a bulk CFT. We show that the broken Ward identities imply very general sum rules on the defect CFT data as well as on the DOE data of bulk operators, which we call defect…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
Motivated by applications to DNA storage, we study reconstruction and list-reconstruction schemes for integer vectors that suffer from limited-magnitude errors. We characterize the asymptotic size of the intersection of error balls in…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
Undersampled inverse problems occur everywhere in the sciences including medical imaging, radar, astronomy etc., yielding underdetermined linear or non-linear reconstruction problems. There are now a myriad of techniques to design decoders…
Limited-angle tomography is a highly ill-posed linear inverse problem. It arises in many applications, such as digital breast tomosynthesis. Reconstructions from limited-angle data typically suffer from severe stretching of features along…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
Time-resolved high-resolution X-ray Computed Tomography (4D $\mu$CT) is an imaging technique that offers insight into the evolution of dynamic processes inside materials that are opaque to visible light. Conventional tomographic…
In this paper, we introduce silhouette tomography, a novel formulation of X-ray computed tomography that relies only on the geometry of the imaging system. We formulate silhouette tomography mathematically and provide a simple method for…
X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered backprojection reconstruction method requires the complete knowledge of the…
SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…