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Subject: search.filters.subject.Finite rate of innovation

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    Magnetic resonance image reconstruction by nullspace based finite rate of innovation framework
    (Association for Computing Machinery, 2021) Sudhakar Reddy, P.S.; Raghavendra, B.S.; Narasimhadhan, A.V.
    The finite rate of innovation (FRI) framework has proved that it is possible to reconstruct the analog signals which have a finite number of parameters. FRI framework is used to reconstruct the images from undersampled magnetic resonance (MR) data. The reconstruction of the MR image from the MR data is a estimation problem, which can be solved by utilizing Prony's method. However, Prony's method involves solving the polynomial roots of the annihilating filter and this fact leads to an unstable reconstruction in the high noise scenario. In this paper, we introduce a novel reconstruction approach is also based on the annihilating filter. However, it involves the use of solutions of an underdetermined linear system. The simulation results of the proposed reconstruction approach show that the peak signal to noise ratio (PSNR) and the structural similarity index measure (SSIM) are higher magnitude than that of conventional FRI methods in the high noise scenario.1 © 2021 ACM.
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    Universal Discrete Finite Rate of Innovation Scheme for Sparse Signal Reconstruction
    (Birkhauser, 2023) Sudhakar Reddy, P.; Raghavendra, B.S.; Narasimhadhan, A.V.
    Finite rate of innovation (FRI) schemes have been proposed to reconstruct a class of discrete-time signals having small number of nonzero coefficients (sparse signals) from a limited number of observations. However, these reconstruction schemes achieve optimal performance up to a certain signal-to-noise ratio (SNR) and breakdown for smaller SNR values. Moreover, these are not universal as they are aware of the number of nonzero coefficients (a.k.a. L0 norm) for reconstruction of the signal. In this paper, we propose a novel FRI reconstruction scheme based on error decrease detector criterion to extend the current scheme to a universal one which enables reconstructing signals with an unknown number of nonzero coefficients. With noiseless conditions, we show that the proposed FRI scheme achieves perfect reconstruction of the original signal. And also, computer simulations for the noisy case are presented where the proposed scheme shows improvements over the traditional FRI scheme in the breakdown SNR. Further, an application of the proposed universal FRI scheme on reconstruction of magnetic resonance images and QRS complexes is demonstrated. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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    Sparse-Prony FRI signal reconstruction
    (Springer Science and Business Media Deutschland GmbH, 2023) Sudhakar Reddy, P.S.; Raghavendra, B.S.; Narasimhadhan, A.V.
    Finite rate of innovation (FRI) approach is used for sampling and reconstruction of a class of non-bandlimited continuous signals having a finite number of free parameters. Traditionally, Prony and matrix-pencil methods are proposed to reconstruct FRI signals from the discrete samples. However, these methods tend to break down at a certain signal-to-noise ratio (SNR). In this paper, we propose sparsity-based annihilating filter, refer it as sparse-Prony, which avoids polynomial root-finding. In the noiseless scenario, the proposed method is able to recover perfectly the original signal. Simulation results for the noisy scenario demonstrate significant improvement in the performance in terms of MSE over the traditional FRI methods, especially in the breakdown SNR. © 2023, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.
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    Approximate Finite Rate of Innovation Based Seismic Reflectivity Estimation
    (Birkhauser, 2024) Sudhakar Reddy, P.S.; Raghavendra, B.S.; Narasimhadhan, A.V.
    Reflectivity inversion is an important deconvolution problem in reflection seismology that helps to describe the subsurface structure. Generally, deconvolution techniques iteratively work on the seismic data for estimating reflectivity. Therefore, these techniques are computationally expensive and may be slow to converge. In this paper, a novel method for estimating reflectivity signals in seismic data using an approximate finite rate of innovation (FRI) framework, is proposed. The seismic data is modeled as a convolution between the Ricker wavelet and the FRI signal, a Dirac impulse train. Relaxing the accurate exponential reproduction limitation given by generalised Strang-Fix (GSF) conditions, we develop a suitable sampling kernel utilizing Ricker wavelet which allows us to estimate the reflectivity signal. The experimental results demonstrate that the proposed approximate FRI framework provides a better reflectivity estimation than the deconvolution technique for medium-to-high signal-to-noise ratio (SNR) regimes with nearly 18% of seismic data. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.