Sparse Sampling of Signal Innovations

Blu, Thierry; Dragotti, Pier Luigi; Vetterli, Martin; Marziliano, Pina; Coulot, L.

doi:10.1109/msp.2007.914998

Cited by 385 publications

(399 citation statements)

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“…Such frameworks have proved to be useful from an implementation point of view by providing simpler interpolation models. The recent theory of finite rate of innovation (FRI) has shown that it is possible to develop exact sampling and reconstruction schemes for specific classes of signals that are neither BL nor belong to a fixed subspace [5], [6]. Signals with FRI are characterized by a set of signal innovations.…”

Section: Reconstruction Of Finite Rate Of Innovationmentioning

confidence: 99%

“…In the absence of noise, perfect reconstruction is achieved using the annihilating filter (AF) method of [6], which is a variation of the well-known Prony's method [17]. However, this method becomes unstable and the accuracy of the reconstruction substantially degrades in the presence of noise.…”

Section: Reconstruction Of Finite Rate Of Innovationmentioning

confidence: 99%

“…A closely related algorithm, the ESPRIT algorithm, was developed as an extension of the state space method [21], [22]. The second approach, known as Cadzow denoising, is based on an iterative procedure that imposes the ideal properties of the FRI samples, namely the rank deficiency of the corresponding system in the AF method and the Toeplitz structure of this system at each iteration [6], [23]. Additionally, these FRI methods can achieve the optimal performance given by the CRLB only above a certain SNR and breaks down at lower SNR.…”

Section: Reconstruction Of Finite Rate Of Innovationmentioning

confidence: 99%

“…For the FRI framework, this is translated in estimating the innovation rate from a set of FRI samples together with the signal innovations. Often, the innovation rate is assumed to be known by the conventional FRI recovery methods and, the standard way to compare the performance of the algorithms is to check the estimation accuracy of the signal innovations against the CRLB [5], [6], [16]. However, this may not be applicable if the true innovation rate or the true signal innovations are unknown.…”

Section: Reconstruction Of Finite Rate Of Innovationmentioning

confidence: 99%

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Reconstruction of Finite Rate of Innovation Signals with Model-Fitting Approach

Dogan

Gilliam

Blu

et al. 2015

IEEE Trans. Signal Process.

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Abstract-Finite rate of innovation (FRI) is a recent framework for sampling and reconstruction of a large class of parametric signals that are characterized by finite number of innovations (parameters) per unit interval. In the absence of noise, exact recovery of FRI signals has been demonstrated. In the noisy scenario, there exist techniques to deal with non-ideal measurements. Yet, the accuracy and resiliency to noise and model mismatch are still challenging problems for real-world applications. We address the reconstruction of FRI signals, specifically a stream of Diracs, from few signal samples degraded by noise and we propose a new FRI reconstruction method that is based on a model-fitting approach related to the structured-TLS problem. The model-fitting method is based on minimizing the training error, that is, the error between the computed and the recovered moments (i.e., the FRI-samples of the signal), subject to an annihilation system. We present our framework for three different constraints of the annihilation system. Moreover, we propose a model order selection framework to determine the innovation rate of the signal; i.e., the number of Diracs by estimating the noise level through the training error curve. We compare the performance of the model-fitting approach with known FRI reconstruction algorithms and Cramér-Rao's lower bound (CRLB) to validate these contributions.Index Terms-Annihilating Filter, Cadzow, Cramér-Rao's lower bound (CRLB), finite-rate-of-innovation, iterative quadratic maximum likelihood (IQML), Kumaresan-Tufts, matrix pencil, model fitting, noise, reconstruction, sampling, structured total least squares (STLS), total least squares (TLS).

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Section: Reconstruction Of Finite Rate Of Innovationmentioning

confidence: 99%

Section: Reconstruction Of Finite Rate Of Innovationmentioning

confidence: 99%

Section: Reconstruction Of Finite Rate Of Innovationmentioning

confidence: 99%

Section: Reconstruction Of Finite Rate Of Innovationmentioning

confidence: 99%

See 2 more Smart Citations

Reconstruction of Finite Rate of Innovation Signals with Model-Fitting Approach

Dogan

Gilliam

Blu

et al. 2015

IEEE Trans. Signal Process.

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“…Recent work in [2] extends the traditional FRI sampling and reconstruction framework [1,13,14,15,16] to a specific class of curves, which are defined implicitly as the roots of certain Fig. 2.…”

Section: Motivation: Fri Curve Annihilationmentioning

confidence: 99%

Annihilation-driven localised image edge models

Pan

Blu

Vetterli

2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We propose a novel edge detection algorithm with sub-pixel accuracy based on annihilation of signals with finite rate of innovation [1,2]. We show that the Fourier domain annihilation equations can be interpreted as spatial domain multiplications. From this new perspective, we obtain an accurate estimation of the edge model by assuming a simple parametric form within each localised block. Further, we build a locally adaptive global mask function (i.e, our edge model) for the whole image. The mask function is then used as an edgepreserving constraint in further processing. Numerical experiments on both edge localisations and image up-sampling show the effectiveness of the proposed approach, which outperforms state-of-the-art method.

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