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X-ray tomography is a reliable tool for determining the inner structure of 3D object with penetrating X-rays. However, traditional reconstruction methods such as FDK require dense angular sampling in the data acquisition phase leading to…
Image restoration requires a careful balance between noise suppression and structure preservation. While first-order total variation (TV) regularization effectively preserves edges, it often introduces staircase artifacts, whereas…
Reconstructing a gene network from high-throughput molecular data is often a challenging task, as the number of parameters to estimate easily is much larger than the sample size. A conventional remedy is to regularize or penalize the model…
Over the last decade or so, reconstruction methods using $\ell_1$ regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The…
Sparse autoencoders (SAEs) are widely used to extract human-interpretable features from neural network activations, but their learned features can vary substantially across random seeds and training choices. To improve stability, we studied…
We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…
High resolution images can be acquired using a non-regular sampling sensor which consists of an underlying low resolution sensor that is covered with a non-regular sampling mask. The reconstructed high resolution image is then obtained…
We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics…
A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a…
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…
Image signals typically are defined on a rectangular two-dimensional grid. However, there exist scenarios where this is not fulfilled and where the image information only is available for a non-regular subset of pixel position. For…
We consider a patch-based learning approach defined in terms of neural networks to estimate spatially adaptive regularisation parameter maps for image denoising with weighted Total Variation (TV) and test it to situations when the noise…
Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This in turn can be achieved by variational regularization…
In many linear regression problems, including ill-posed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a classical path is to use $\ell_{12}$ block…
Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the…
We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…
Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing…
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…
We propose a general learning based framework for solving nonsmooth and nonconvex image reconstruction problems. We model the regularization function as the composition of the $l_{2,1}$ norm and a smooth but nonconvex feature mapping…
Electrical capacitance tomography (ECT) has been investigated in many fields due to its advantages of being non-invasive and low cost. Sparse algorithms with l1-norm regularization are used to reduce the smoothing effect and obtain sharp…