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Register a new userConditional Expressions for Blind Deconvolution: Derivative form
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Added by
Ikuo Moritani
Publication date
2006
fields
Informatics Engineering
and research's language is
English
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We developed novel conditional expressions (CEs) for Lane and Bates blind deconvolution. The CEs are given in term of the derivatives of the zero-values of the z-transform of given images. The CEs make it possible to automatically detect multiple blur convolved in the given images all at once without performing any analysis of the zero-sheets of the given images. We illustrate the multiple blur-detection by the CEs for a model image
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We present conditional expression (CE) for finding blurs convolved in given images. The CE is given in terms of the zero-values of the blurs evaluated at multi-point. The CE can detect multiple blur all at once. We illustrate the multiple blur-detection by using a test image.
We revisit the Blind Deconvolution problem with a focus on understanding its robustness and convergence properties. Provable robustness to noise and other perturbations is receiving recent interest in vision, from obtaining immunity to adversarial attacks to assessing and describing failure modes of algorithms in mission critical applications. Further, many blind deconvolution methods based on deep architectures internally make use of or optimize the basic formulation, so a clearer understanding of how this sub-module behaves, when it can be solved, and what noise injection it can tolerate is a first order requirement. We derive new insights into the theoretical underpinnings of blind deconvolution. The algorithm that emerges has nice convergence guarantees and is provably robust in a sense we formalize in the paper. Interestingly, these technical results play out very well in practice, where on standard datasets our algorithm yields results competitive with or superior to the state of the art. Keywords: blind deconvolution, robust continuous optimization
In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns than knowns . Nevertheless, this problem arises in many application fields; and empirically, some of these fields have had success using heuristic methods -- even economically very important ones, in wireless communications and oil exploration. Todays fashionable heuristic formulations pose non-convex optimization problems which are then attacked heuristically as well. The fact that blind deconvolution can be solved under some repeatable and naturally-occurring circumstances poses a theoretical puzzle. To bridge the gulf between reported successes and theorys limited understanding, we exhibit a convex optimization problem that -- assuming signal sparsity -- can convert a crude approximation to the true filter into a high-accuracy recovery of the true filter. Our proposed formulation is based on L1 minimization of inverse filter outputs. We give sharp guarantees on performance of the minimizer assuming sparsity of signal, showing that our proposal precisely recovers the true inverse filter, up to shift and rescaling. There is a sparsity/initial accuracy tradeoff: the less accurate the initial approximation, the greater we rely on sparsity to enable exact recovery. To our knowledge this is the first reported tradeoff of this kind. We consider it surprising that this tradeoff is independent of dimension. We also develop finite-$N$ guarantees, for highly accurate reconstruction under $Ngeq O(k log(k) )$ with high probability. We further show stable approximation when the true inverse filter is infinitely long and extend our guarantees to the case where the observations are contaminated by stochastic or adversarial noise.
Although single-image super-resolution (SISR) methods have achieved great success on single degradation, they still suffer performance drop with multiple degrading effects in real scenarios. Recently, some blind and non-blind models for multiple degradations have been explored. However, those methods usually degrade significantly for distribution shifts between the training and test data. Towards this end, we propose a conditional meta-network framework (named CMDSR) for the first time, which helps SR framework learn how to adapt to changes in input distribution. We extract degradation prior at task-level with the proposed ConditionNet, which will be used to adapt the parameters of the basic SR network (BaseNet). Specifically, the ConditionNet of our framework first learns the degradation prior from a support set, which is composed of a series of degraded image patches from the same task. Then the adaptive BaseNet rapidly shifts its parameters according to the conditional features. Moreover, in order to better extract degradation prior, we propose a task contrastive loss to decrease the inner-task distance and increase the cross-task distance between task-level features. Without predefining degradation maps, our blind framework can conduct one single parameter update to yield considerable SR results. Extensive experiments demonstrate the effectiveness of CMDSR over various blind, even non-blind methods. The flexible BaseNet structure also reveals that CMDSR can be a general framework for large series of SISR models.
We propose a blind deconvolution method for signals on graphs, with the exact sparseness constraint for the original signal. Graph blind deconvolution is an algorithm for estimating the original signal on a graph from a set of blurred and noisy measurements. Imposing a constraint on the number of nonzero elements is desirable for many different applications. This paper deals with the problem with constraints placed on the exact number of original sources, which is given by an optimization problem with an $ell_0$ norm constraint. We solve this non-convex optimization problem using the ADMM iterative solver. Numerical experiments using synthetic signals demonstrate the effectiveness of the proposed method.
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