Related papers: Single-angle Radon samples based reconstruction of…
The act of measuring a physical signal or field suggests a generalization of the wavelet transform that turns out to be a windowed version of the Radon transform. A reconstruction formula is derived which inverts this transform. A special…
We find a new and simple inversion formula of the Radon transform RT with the only use of the shearlet system and of well-known properties of RT. No intertwining relation of differential operators in Euclidean space and Radon domain is…
Magnetic Resonance Imaging (MRI) produces excellent soft tissue contrast, albeit it is an inherently slow imaging modality. Promising deep learning methods have recently been proposed to reconstruct accelerated MRI scans. However, existing…
Compton scatter tomography is an emerging technique with attractive applications in several fields in imaging such as non-destructive testing and medical scanning. In this paper, we introduce a novel modality in three dimensions with a…
This work introduces a novel reinterpretation of structured illumination (SI) microscopy for coherent imaging that allows three-dimensional imaging of complex refractive index (RI). To do so, we show that coherent SI is mathematically…
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…
Intrinsic decomposition from a single image is a highly challenging task, due to its inherent ambiguity and the scarcity of training data. In contrast to traditional fully supervised learning approaches, in this paper we propose learning…
Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere) transform, we develop a data-driven Saak (Subspace approximation with augmented kernels) transform in this work. The Saak transform consists of three steps: 1)…
We introduce a deep learning (DL) framework for inverse problems in imaging, and demonstrate the advantages and applicability of this approach in passive synthetic aperture radar (SAR) image reconstruction. We interpret image recon-…
Single image super-resolution (SISR) is a very popular topic nowadays, which has both research value and practical value. In daily life, we crop a large image into sub-images to do super-resolution and then merge them together. Although…
In this work we introduce a new Radon transform which arises from a new modality of Compton Scattering Tomography (CST). This new system is made of a single detector rotating around a fixed source. Unlike some previous CST, no collimator is…
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…
In [J. Bures, R. Lavicka, V. Soucek, Elements of quaternionic analysis and Radon transform, Textos de Matematica 42, Departamento de Matematica, Universidade de Coimbra, 2009], the authors describe a link between holomorphic functions…
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…
In this paper, we investigate the relations between the Radon and weighted divergent beam and cone transforms. Novel inversion formulas are derived for the latter two. The weighted cone transform arises, for instance, in image…
Rotating-view thick-slice acquisition is highly SNR-efficient for mesoscale diffusion MRI (dMRI) but requires numerous rotating views to satisfy Nyquist sampling, resulting in long scan time. We propose a self-supervised Spatial-Angular…
We propose SinIR, an efficient reconstruction-based framework trained on a single natural image for general image manipulation, including super-resolution, editing, harmonization, paint-to-image, photo-realistic style transfer, and artistic…
To reduce scanning time and/or improve spatial/temporal resolution in some MRI applications, parallel MRI (pMRI) acquisition techniques with multiple coils acquisition have emerged since the early 1990s as powerful 3D imaging methods that…
Tomography is a central tool in medical applications, allowing doctors to investigate patients' interior features. The Radon transform (in two dimensions) is commonly used to model the measurement process in parallel-beam CT. Suitable…
In radio astronomy, the challenge of reconstructing a sky map from time ordered data (TOD) is known as an inverse problem. Standard map-making techniques and gridding algorithms are commonly employed to address this problem, each offering…