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Recent work introduced a framework for signal processing (SP) on meet/join lattices. Such a lattice is partially ordered and supports a meet (or join) operation that returns the greatest lower bound and the smallest upper bound of two elements, respectively. Lattices appear in various domains and can be used, for example, to express rankings in social choice theory or multisets in combinatorial auctions. Discrete lattice SP (DLSP) uses the meet operation as shift and derives associated notions of convolution and Fourier transform for signals indexed by lattices.

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Design of infinite impulse response (IIR) digital filters to approximate some desired magnitude-frequency response is a classical research topic in signal processing. When a pole radius constraint is imposed, however, the problem becomes challenging and few solution methods are available. This paper converts the magnitude-response approximation problem into another problem that approximates the desired magnitude response and an accompanied phase response simultaneously.

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The mean curvature has been shown a proper regularization in various ill-posed inverse problems in signal processing. Traditional solvers are based on either gradient descent methods or Euler Lagrange Equation. However, it is not clear if this mean curvature regularization term itself is convex or not. In this paper, we first prove that the mean curvature regularization is convex if the dimension of imaging domain is not

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In [doi{10.1109/ICMEW.2014.6890711}], a~graph-based filtering of noisy images is performed by directly computing a projection of the image to be filtered onto a lower dimensional Krylov subspace of the graph Laplacian, constructed using non-negative graph weights determined by distances between image data corresponding to image pixels. We extend the construction of the graph Laplacian to the case, where some graph weights can be negative.

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The most efficient signal edge-preserving smoothing filters, e.g., for denoising, are non-linear. Thus, their acceleration is challenging and is often done in practice by tuning filters parameters, such as increasing the width of the local smoothing neighborhood, resulting in more aggressive smoothing of a single sweep at the cost of increased edge blurring. We propose an alternative technology, accelerating the original filters without tuning, by running them through a conjugate gradient method, not affecting their quality.

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Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the bilateral and guided filters. We propose constructing accelerated polynomial filters by running flexible Krylov subspace based linear and eigenvalue solvers such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG) method.

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Several problems in signal processing and machine learning can be casted as optimization problems. In many cases, they are of large-scale, nonlinear, have constraints, and nonsmooth in the unknown parameters. There exists plethora of fast algorithms for smooth convex optimization, but these algorithms are not readily applicable to nonsmooth problems, which has led to a considerable amount of research in this direction. In this paper, we propose a general algorithm for nonsmooth bound-constrained convex optimization problems.

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