Related papers: Introduction of total variation regularization int…
The method of filtered back projection (FBP) is a widely used reconstruction technique in X-ray computerized tomography (CT), which is particularly important in clinical diagnostics. To reduce scanning times and radiation doses in medical…
Filtered backprojection (FBP) is an efficient and popular class of tomographic image reconstruction methods. In photoacoustic tomography, these algorithms are based on theoretically exact analytic inversion formulas which results in…
Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy…
Filtered back projection (FBP) is a commonly used technique in tomographic image reconstruction demonstrating acceptable quality. The classical direct implementations of this algorithm require the execution of $\Theta(N^3)$ operations,…
The aim of this paper is to test and analyze a novel technique for image reconstruction in positron emission tomography, which is based on (total variation) regularization on both the image space and the projection space. We formulate our…
In the past decade, sparsity-driven regularization has led to advancement of image reconstruction algorithms. Traditionally, such regularizers rely on analytical models of sparsity (e.g. total variation (TV)). However, more recent methods…
The use of ray projections to reconstruct images is a common technique in medical imaging. Dealing with incomplete data is particularly important when a patient is vulnerable to potentially damaging radiation or is unable to cope with the…
While filtered back projection (FBP) is still the method of choice for fast tomographic reconstruction, its performance degrades noticeably in the presence of noise, incomplete sampling, or non-standard scan geometries. We propose a…
For conventional computed tomography (CT) image reconstruction tasks, the most popular method is the so-called filtered-back-projection (FBP) algorithm. In it, the acquired Radon projections are usually filtered first by a ramp kernel…
Filtered back projection (FBP) methods are the most widely used reconstruction algorithms in computerized tomography (CT). The ill-posedness of this inverse problem allows only an approximate reconstruction for given noisy data. Studying…
Filtered backpropagation (FBPP) is a well-known technique used for Diffraction Tomography (DT). For accurate reconstruction of a complex image using FBPP, full $360^{\circ}$ angular coverage is necessary. However, it has been shown that…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
Purpose: Iterative projection reconstruction algorithms are currently the preferred reconstruction method in proton computed tomography (pCT). However, due to inconsistencies in the measured data arising from proton energy straggling and…
A Bayesian hierarchical model for total variation regularisation is presented in this paper. All the parameters of an inverse problem, including the "regularisation parameter", are estimated simultaneously from the data in the model. The…
While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or…
In the past decade, sparsity-driven regularization has led to significant improvements in image reconstruction. Traditional regularizers, such as total variation (TV), rely on analytical models of sparsity. However, increasingly the field…
Improving the quality of positron emission tomography (PET) images, affected by low resolution and high level of noise, is a challenging task in nuclear medicine and radiotherapy. This work proposes a restoration method, achieved after…
Non-uniqueness and instability are characteristic features of image reconstruction processes. As a result, it is necessary to develop regularization methods that can be used to compute reliable approximate solutions. A regularization method…
Filtered back projection (FBP) is a classical method for image reconstruction from sinogram CT data. FBP is computationally efficient but produces lower quality reconstructions than more sophisticated iterative methods, particularly when…
The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii)…