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We derive a memory-efficient first-order variable splitting algorithm for convex image reconstruction problems with non-smooth regularization terms. The algorithm is based on a primal-dual approach, where one of the dual variables is…
Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
This paper investigates the problem of recovering hyperspectral (HS) images from single RGB images. To tackle such a severely ill-posed problem, we propose a physically-interpretable, compact, efficient, and end-to-end learning-based…
Multi-category support vector machine (MC-SVM) is one of the most popular machine learning algorithms. There are lots of variants of MC-SVM, although different optimization algorithms were developed for different learning machines. In this…
We consider convex optimization problems which are widely used as convex relaxations for low-rank matrix recovery problems. In particular, in several important problems, such as phase retrieval and robust PCA, the underlying assumption in…
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…
In the previous blind deconvolution methods, de-blurred images can be obtained by using the edge or pixel information. However, the existing edge-based methods did not take advantage of edge information in ommi-directions, but only used…
We consider continuous-time dynamics for distributed optimization with set constraints in the paper. To handle the computational complexity of projection-based dynamics due to solving a general quadratic optimization subproblem with…
We propose a novel and efficient training method for RNNs by iteratively seeking a local minima on the loss surface within a small region, and leverage this directional vector for the update, in an outer-loop. We propose to utilize the…
We use the Richardson-Lucy deconvolution algorithm to extract one dimensional (1D) spectra from LAMOST spectrum images. Compared with other deconvolution algorithms, this algorithm is much more fast. The practice on a real LAMOST image…
Domain knowledge is useful to improve the generalization performance of learning machines. Sign constraints are a handy representation to combine domain knowledge with learning machine. In this paper, we consider constraining the signs of…
The Frank-Wolfe (FW) optimization algorithm has lately re-gained popularity thanks in particular to its ability to nicely handle the structured constraints appearing in machine learning applications. However, its convergence rate is known…
Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive…
The co-localization problem is a model that simultaneously localizes objects of the same class within a series of images or videos. In \cite{joulin2014efficient}, authors present new variants of the Frank-Wolfe algorithm (aka conditional…
Recent progress in robust statistical learning has mainly tackled convex problems, like mean estimation or linear regression, with non-convex challenges receiving less attention. Phase retrieval exemplifies such a non-convex problem,…
We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix $X$. This setting arises naturally in applications from…
An extension of the Frank-Wolfe Algorithm (FWA), also known as Conditional Gradient algorithm, is proposed. In its standard form, the FWA allows to solve constrained optimization problems involving $\beta$-smooth cost functions, calling at…
Schlieren deflectometry aims at characterizing the deflections undergone by refracted incident light rays at any surface point of a transparent object. For smooth surfaces, each surface location is actually associated with a sparse…
Recent advances in Schramm-Loewner evolution have driven increasing interest in non-standard Loewner flows. In this work, we propose a novel splitting algorithm to simulate random Loewner curves with rigorous convergence analysis in…