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For ghost imaging, pursuing high resolution images and short acquisition times required for reconstructing images are always two main goals. We report an image reconstruction algorithm called compressive sampling (CS) reconstruction to…
The amount of large-scale real data around us increase in size very quickly and so does the necessity to reduce its size by obtaining a representative sample. Such sample allows us to use a great variety of analytical methods, whose direct…
Maximum-likelihood methods are applied to the problem of absorption tomography. The reconstruction is done with the help of an iterative algorithm. We show how the statistics of the illuminating beam can be incorporated into the…
In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling…
The structure of Magnetic Resonance Images (MRI) and especially their compressibility in an appropriate representation basis enables the application of the compressive sensing theory, which guarantees exact image recovery from incomplete…
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon,…
We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to…
A concept of defining images based on its own approximate ones is proposed here, which is called 'Self-ception'. In this regard, an algorithm is proposed to implement the self-ception for images, which we call it 'Image Self-ception' since…
Is it possible to detect a feature in an image without ever looking at it? Images are known to have sparser representation in Wavelets and other similar transforms. Compressed Sensing is a technique which proposes simultaneous acquisition…
We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…
We address the problem of image reconstruction from incomplete measurements, encompassing both upsampling and inpainting, within a learning-based framework. Conventional supervised approaches require fully sampled ground truth data, while…
Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to achieve this. It was justified recently from a theoretical point of view in the…
Assume that samples of a filtered version of a function in a shift-invariant space are avalaible. This work deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support.…
Quarter sampling is a novel sensor concept that enables the acquisition of higher resolution images without increasing the number of pixels. This is achieved by covering three quarters of each pixel of a low-resolution sensor such that only…
Recently it has been shown that precise dose control and an increase in the overall acquisition speed of atomic resolution scanning transmission electron microscope (STEM) images can be achieved by acquiring only a small fraction of the…
Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image,…
An accurate method for warping images is presented. Differently from most commonly used techniques, this method guarantees the conservation of the intensity of the transformed image, evaluated as the sum of its pixel values over the whole…
Ptychography is a well-studied phase imaging method that makes non-invasive imaging possible at a nanometer scale. It has developed into a mainstream technique with various applications across a range of areas such as material science or…
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…
The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long…