Super-resolution through Error Energy Reduction

By R. Gerchberg. 1974

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Designing structured tight frames via an alternating projection method (2005, methodology): “In the ﬁeld of signal restoration and recovery, we mention the work of Landau–Miranker [98], Gerchberg [99], Youla–Webb [100], Cadzow [95], and Donoho–Stark [101].”
A limited-angle CT reconstruction method based on anisotropic TV minimization (2013, methodology): “One direction is to develop new reconstruction algorithms such as iterative reconstruction re-projection, Gerchberg–Papoulis, singular value decomposition, wavelet decomposition, projections onto convex sets (POCS) and so on (Nassi et al 1982, Gerchberg 1974, Natterer 2001, Candes and Romberg 2005).”
Signal Recovery by Proximal Forward-Backward Splitting (2005, result): “In that paper, the problem was to ﬁnd a signal x in a closed vector subspace C , knowing its projection p onto a closed vector subspace V (hence L = P V and Q = { p } ); it was also observed that the standard signal extrapolation schemes of Gerchberg [37] and Papoulis [59] ﬁtted this framework.”
Deconvolution in Astronomy: A Review (2002, methodology): “The Gerchberg-Saxon-Papoulis (Gerchberg 1974) method is iterative and uses the a priori information on the object, which is its positivity and its support in the spatial domain.”
The Hybrid Steepest Descent Method for the Variational Inequality Problem over the Intersection of Fixed Point Sets of Nonexpansive Mappings (2001, background): “band-limited extrapolation with subspace constraints [54, 71, 83, 86], (ii) image reconstruction with positivity constraint [62, 96–99, 114, 115], and (iii) signal recovery (or design) [4, 64, 81, 86, 94, 95] accompanied by constraints on amplitude, support, energy etc.”
Super-resolution: a comprehensive survey (2014, methodology): “Frequency (Fourier) [1], [2], [3], [9], [11], [12], [15], [17], [19], [21], [46], [52], [59], [67], [68], [69], [70], [103], [104], [110], [120], [137], [119], [126], [141], [144], [145], [161], [178], [197], [201], [211], [219], [221], [267], [321], [351], [356], [359], [487], [358], [370], [390], ”
Foundations of Signal Processing (2014, methodology): “Iterative reconstruction algorithms The alternating projection algorithm was introduced and analyzed by Cheney and Goldstein [13]; Papoulis [75] and Gerchberg [33] popularized it for reconstruction of bandlimited signals.”
A novel scheme for the solution of the time-domain integral equations of electromagnetics (2004, background): “Here, the function to be extrapolated is known to be bandlimited, and there exists a voluminous literature on the extrapolation of bandlimited functions (see, for example, [31]–[33]).”
GESPAR: Efficient Phase Retrieval of Sparse Signals (2013, background): “A variety of methods have been developed that use such prior information, which may be the signal’s support (region in which the signal is nonzero), non-negativity, or the signal’s magnitude [4], [5].”