Superresolution via sparsity constraints

By David L. Donoho. 1992

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Citations in the corpus

On a Link Between Kernel Mean Maps and Fraunhofer Diffraction, with an Application to Super-Resolution Beyond the Diffraction Limit (2013, background): “Another possible constraint is sparsity: Donoho [6] studied the problem of recovering a sparse signal for which only low frequencies of its Fourier transform are available.”
Exact Support Recovery for Sparse Spikes Deconvolution (2013, unknown): “They were later studied in depth by David Donoho and co-workers, see for instance [14].”
Stable recovery of sparse overcomplete representations in the presence of noise (2006, background): “The careful theoretical work on superresolution [10] explains that stable superresolution is possible using sparsity; however, the notion of sparsity needs to be adapted to the setting.”
Towards a Mathematical Theory of Super‐resolution (2012, result): “As to results regarding the robustness of super-resolution in the presence of noise, Donoho [11] studies the modulus of continuity of the recovery of a signed measure on a discrete lattice from its spectrum on the interval Œ fc ; fc , a setting that is also equivalent to that of Corollary 1.4 when t”
Minimization of ℓ1-2 for Compressed Sensing (2015, methodology): “For traditional inversion methods to work, it is necessary for L to be at least 1 Rayleigh length (RL) which is unity in the frequency domain [25, 20].”
Super-Resolution from Noisy Data (2012, unknown): “5 Related Work Earlier work on the super-resolution problem in the presence of noise studied under which conditions recovery is not hopelessly ill-posed, establishing that sparsity is not sufficient even for signals supported on a grid [9, 39].”
Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints (2007, unknown): “The use of sparsity in inverse problems for data recovery is the most recent step of this concept’s long career of “simplifying and understanding complexity”, with an enormous potential in applications [2, 9, 15, 18, 20, 21, 22, 24, 23, 31, 33, 32, 35, 37, 41].”
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint (2003, unknown): “The key role played by sparsity to achieve superresolution in diﬀraction-limited imaging was already emphasized by Donoho [14] more than a decade ago.”
A sparse signal reconstruction perspective for source localization with sensor arrays (2005, background): “…code with odd length N, the automorphism group contains the following two subgroups: 0S : The set of permutations 0 1 1, ,..., N , where :k j j k mod N. 1S : The set of permutations 0 1 1, ,..., N , where : 2k kj j mod N and 1m is the smallest positive integer such that 12 1m mod N. 3”
Modern regularization methods for inverse problems (2018, methodology): “r investigating regularization methods in Banach spaces became ideas of sparsity including wavelet shrinkage and the variational counterpart of regularization ‘1-type norms, e.g. in Besov spaces (cf. [144, 147]). This led in parallel to the eld of compressed sensing, where the focus was rather on de”