Related papers: Controlled Wavelet Domain Sparsity in X-ray Tomogr…
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An…
A computational method is introduced for choosing the regularization parameter for total variation (TV) regularization. The approach is based on computing reconstructions at a few different resolutions and various values of regularization…
This work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systems pose a challenge for iterative image…
We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its…
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…
The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
We propose a sparse reconstruction framework for solving inverse problems. Opposed to existing sparse regularization techniques that are based on frame representations, we train an encoder-decoder network by including an $\ell^1$-penalty.…
Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in…
We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…
The inversion of electromagnetic induction data to a conductivity profile is an ill-posed problem. Regularization improves the stability of the inversion and, based on Occam's razor principle, a smoothing constraint is typically used.…
In dynamic MRI, sufficient time resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based image…
Denoising by frame thresholding is one of the most basic and efficient methods for recovering a discrete signal or image from data that are corrupted by additive Gaussian white noise. The basic idea is to select a frame of analyzing…
Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…
We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…
We propose a variable smoothing algorithm for solving nonconvexly constrained nonsmooth optimization problems. The target problem has two issues that need to be addressed: (i) the nonconvex constraint and (ii) the nonsmooth term. To handle…
In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
This paper is concerned with variational and Bayesian approaches to neuro-electromagnetic inverse problems (EEG and MEG). The strong indeterminacy of these problems is tackled by introducing sparsity inducing regularization/priors in a…