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Large pre-trained transformers have revolutionized artificial intelligence across various domains, and fine-tuning remains the dominant approach for adapting these models to downstream tasks due to the cost of training from scratch.…
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…
We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the…
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
Restoration of digital images from their degraded measurements has always been a problem of great theoretical and practical importance in numerous applications of imaging sciences. A specific solution to the problem of image restoration is…
We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta…
We describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images. We first construct a nonnegative dictionary based on prototype elements from the…
This paper presents an adaptive image sampling algorithm based on Deep Learning (DL). The adaptive sampling mask generation network is jointly trained with an image inpainting network. The sampling rate is controlled in the mask generation…
Reliably reconstructing physical fields from sparse sensor data is a challenge that frequently arises in many scientific domains. In practice, the process generating the data often is not understood to sufficient accuracy. Therefore, there…
We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…
Turbulence-degraded image frames are distorted by both turbulent deformations and space-time-varying blurs. To suppress these effects, we propose a multi-frame reconstruction scheme to recover a latent image from the observed image…
Objective: We propose a method for the reconstruction of parameter-maps in Quantitative Magnetic Resonance Imaging (QMRI). Methods: Because different quantitative parameter-maps differ from each other in terms of local features, we propose…
Phaseless diffraction measurements recorded by a CCD detector are often affected by Poisson noise. In this paper, we propose a dictionary learning model by employing patches based sparsity to denoise Poisson phaseless measurement. The model…
Reconstructing high-quality magnetic resonance images (MRI) from undersampled raw data is of great interest from both technical and clinical point of views. To this date, however, it is still a mathematically and computationally challenging…
Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem encountered in compressive sensing, where one seeks to…
High-velocity streams of high-dimensional data pose significant "big data" analysis challenges across a range of applications and settings. Online learning and online convex programming play a significant role in the rapid recovery of…
In this paper, the problem of Magnetic Resonance (MR) image reconstruction from partial Fourier samples has been considered. To this aim, we leverage the evidence that MR images are sparser than their zero-filled reconstructed ones from…
This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called "Sparse Signal Subspace Decomposition" (or 3SD) method. This method makes use of a novel criterion based on the…
Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally,…