160 research outputs found
Non-smooth Non-convex Bregman Minimization: Unification and new Algorithms
We propose a unifying algorithm for non-smooth non-convex optimization. The
algorithm approximates the objective function by a convex model function and
finds an approximate (Bregman) proximal point of the convex model. This
approximate minimizer of the model function yields a descent direction, along
which the next iterate is found. Complemented with an Armijo-like line search
strategy, we obtain a flexible algorithm for which we prove (subsequential)
convergence to a stationary point under weak assumptions on the growth of the
model function error. Special instances of the algorithm with a Euclidean
distance function are, for example, Gradient Descent, Forward--Backward
Splitting, ProxDescent, without the common requirement of a "Lipschitz
continuous gradient". In addition, we consider a broad class of Bregman
distance functions (generated by Legendre functions) replacing the Euclidean
distance. The algorithm has a wide range of applications including many linear
and non-linear inverse problems in signal/image processing and machine
learning
Geometry-Aware Neighborhood Search for Learning Local Models for Image Reconstruction
Local learning of sparse image models has proven to be very effective to
solve inverse problems in many computer vision applications. To learn such
models, the data samples are often clustered using the K-means algorithm with
the Euclidean distance as a dissimilarity metric. However, the Euclidean
distance may not always be a good dissimilarity measure for comparing data
samples lying on a manifold. In this paper, we propose two algorithms for
determining a local subset of training samples from which a good local model
can be computed for reconstructing a given input test sample, where we take
into account the underlying geometry of the data. The first algorithm, called
Adaptive Geometry-driven Nearest Neighbor search (AGNN), is an adaptive scheme
which can be seen as an out-of-sample extension of the replicator graph
clustering method for local model learning. The second method, called
Geometry-driven Overlapping Clusters (GOC), is a less complex nonadaptive
alternative for training subset selection. The proposed AGNN and GOC methods
are evaluated in image super-resolution, deblurring and denoising applications
and shown to outperform spectral clustering, soft clustering, and geodesic
distance based subset selection in most settings.Comment: 15 pages, 10 figures and 5 table
Image Restoration for Remote Sensing: Overview and Toolbox
Remote sensing provides valuable information about objects or areas from a
distance in either active (e.g., RADAR and LiDAR) or passive (e.g.,
multispectral and hyperspectral) modes. The quality of data acquired by
remotely sensed imaging sensors (both active and passive) is often degraded by
a variety of noise types and artifacts. Image restoration, which is a vibrant
field of research in the remote sensing community, is the task of recovering
the true unknown image from the degraded observed image. Each imaging sensor
induces unique noise types and artifacts into the observed image. This fact has
led to the expansion of restoration techniques in different paths according to
each sensor type. This review paper brings together the advances of image
restoration techniques with particular focuses on synthetic aperture radar and
hyperspectral images as the most active sub-fields of image restoration in the
remote sensing community. We, therefore, provide a comprehensive,
discipline-specific starting point for researchers at different levels (i.e.,
students, researchers, and senior researchers) willing to investigate the
vibrant topic of data restoration by supplying sufficient detail and
references. Additionally, this review paper accompanies a toolbox to provide a
platform to encourage interested students and researchers in the field to
further explore the restoration techniques and fast-forward the community. The
toolboxes are provided in https://github.com/ImageRestorationToolbox.Comment: This paper is under review in GRS
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