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A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and…
Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…
We introduce a class of higher-order anisotropic total variation regularisers, which are defined for possibly inhomogeneous, smooth elliptic anisotropies, that extends the Total Generalized Variation (TGV) regulariser and its variants. We…
The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography. To this aim, we use models for acoustic wave propagation…
Online and stochastic gradient methods have emerged as potent tools in large scale optimization with both smooth convex and nonsmooth convex problems from the classes $C^{1,1}(\reals^p)$ and $C^{1,0}(\reals^p)$ respectively. However to our…
In the fields of image restoration and image fusion, model-driven methods and data-driven methods are the two representative frameworks. However, both approaches have their respective advantages and disadvantages. The model-driven methods…
Curve evolution schemes for image segmentation based on a region based contour model allowing for junctions, vector-valued images and topology changes are introduced. Together with an a posteriori denoising in the segmented homogeneous…
The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…
Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly…
Many techniques have been proposed for image reconstruction in medical imaging that aim to recover high-quality images especially from limited or corrupted measurements. Model-based reconstruction methods have been particularly popular…
Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier,…
Medical imaging modalities have revolutionized health-care approaches by offering a better understanding of the human anatomy. Discovery of x-rays allowed the exploiting of the micro-scaled information of human anatomy. Computed tomography…
Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity…
We present two methods that combine image reconstruction and edge detection in computed tomography (CT) scans. Our first method is as an extension of the prominent filtered backprojection algorithm. In our second method we employ…
Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…
A rotational modulator (RM) gamma-ray imager is capable of obtaining significantly better angular resolution than the fundamental geometric resolution defined by the ratio of detector diameter to mask-detector separation. An RM imager…
We use a spatial light modulator in a diffraction tomographic system to assess the accuracy of different refractive index reconstruction algorithms. Optical phase conjugation principles through complex media, allows us to quantify the error…
Image processing techniques has been widely used in dental researches such as human identification and forensic dentistry, teeth numbering, dental carries detection and periodontal disease analysis. One of the most challenging parts in…
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal…