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This paper addresses the problem of the interpolation of 2-d spherical signals from non-uniformly sampled and noisy data. We propose a graph-based regularization algorithm to improve the signal reconstructed by local interpolation methods such as nearest neighbour or kernel-based interpolation algorithms. We represent the signal as a function on a graph where weights are adapted to the particular...
Recent results in compressed sensing show that a sparse or compressible signal can be reconstructed from a few incoherent measurements. Compressive sensing systems are not immune to noise, which is always present in practical acquisition systems. In this paper we propose robust methods for sampling and reconstructing sparse signals in the presence of impulsive noise. Analysis of the proposed methods...
In this paper we evaluate several methods of reconstructing signals from finite sets of their samples. A class of band-limited signals is considered. Both, noise-free and noisy cases are studied. The evaluation is performed by extensive simulations where different shapes and bandwidths of the reconstructing filters are examined. We demonstrate that if a fixed number of signal samples are used in the...
In this paper we present a powerful approach for noisy data reconstruction and also for data compression based on our algorithms for tensor factorization and decomposition [10], [9]. This approach has many potential applications in computational neuroscience, multi-sensory, multidimensional data analysis and text mining. Our algorithms are locally stable and work well for sufficiently sparse data...
We consider the problem of recovering sparse phenomena from projections of noisy data, a topic of interest in compressed sensing. We describe the problem in terms of sensing capacity, which we define as the supremum of the ratio of the number of signal dimensions that can be identified per projection. This notion quantifies minimum number of observations required to estimate a signal as a function...
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