Image reconstruction by deterministic compressed sensing with chirp matrices

Ni, Kang-Yu; Mahanti, P.; Datta, Somantika; Roudenko, Svetlana; Cochran, Douglas

doi:10.1117/12.832649

Cited by 8 publications

(11 citation statements)

References 13 publications

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“…Moreover, such reconstruction should be stable under noise and also work when the signal is non-sparse. In this paper, we discuss the stability and robustness of the algorithms we introduced in [3]. We show that these algorithms are stable for non-sparse (compressible) signals and robust under various types of noise.…”

Section: N Nmentioning

confidence: 99%

“…We show that these algorithms are stable for non-sparse (compressible) signals and robust under various types of noise. In addition, we also indicate how, when using the sensing matrix composed from Reed-Muller sequences, the algorithms in [3] may be modified to efficiently handle excessively large images or large 2D signals.…”

Section: N Nmentioning

confidence: 99%

“…This paper is structured as follows: in Section 2, we review our reconstruction algorithm of [3] and comment on how to incorporate properties of the Reed-Muller sequences so that the algorithm can handle images of size much larger than considered so far. Then we discuss how to choose the proper wavelet domain and the level of decomposition of the image under the chosen wavelet basis.…”

Section: N Nmentioning

confidence: 99%

“…A similar reconstruction algorithm was also proposed for a sensing matrix made from Reed-Muller sequences [16]. In [3], we proposed new reconstruction algorithms for deterministic sensing matrices made from chirp and Reed-Muller sequences that are suitable for 2D images. The advantage of using deterministic matrices for compressed sensing is that reconstruction can be very efficient [15,16].…”

Section: Introductionmentioning

confidence: 99%

“…This is because the locations of the nonzero coefficients, usually in the wavelet domain, are not distributed uniformly. Our proposed algorithm [3] takes this into account and we have shown that it outperforms a standard compressed sensing method, which takes random noiselet measurements and uses minimization for reconstruction, for example, see [19]. 1  Authors in [17] also derived that the deterministic sensing matrices are resilient to noise.…”

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confidence: 99%

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Stability of Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Sequences

Datta¹,

Ni²,

Mahanti³

et al. 2013

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We explore the stability of image reconstruction algorithms under deterministic compressed sensing. Recently, we have proposed [1-3] deterministic compressed sensing algorithms for 2D images. These algorithms are suitable when Daubechies wavelets are used as the sparsifying basis. In the initial work, we have shown that the algorithms perform well for images with sparse wavelets coefficients. In this work, we address the question of robustness and stability of the algorithms, specifically, if the image is not sparse and/or if noise is present. We show that our algorithms perform very well in the presence of a certain degree of noise. This is especially important for MRI and other real world applications where some level of noise is always present.

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Section: N Nmentioning

confidence: 99%

Section: N Nmentioning

confidence: 99%

Section: N Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Stability of Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Sequences

Datta¹,

Ni²,

Mahanti³

et al. 2013

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Compressed sensing reconstruction using expectation propagation

Braunstein¹,

Muntoni²,

Pagnani³

et al. 2020

J. Phys. A: Math. Theor.

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Many interesting problems in fields ranging from telecommunications to computational biology can be formalized in terms of large underdetermined systems of linear equations with additional constraints or regularizers. One of the most studied, the compressed sensing problem, consists in finding the solution with the smallest number of non-zero components of a given system of linear equations y = Fw for known measurement vector y and sensing matrix F. Here, we will address the compressed sensing problem within a Bayesian inference framework where the sparsity constraint is remapped into a singular prior distribution (called Spike-and-Slab or Bernoulli-Gauss). A solution to the problem is attempted through the computation of marginal distributions via expectation propagation, an iterative computational scheme originally developed in statistical physics. We will show that this strategy is more accurate for statistically correlated measurement matrices. For computational strategies based on the Bayesian framework such as variants of belief propagation, this is to be expected, as they implicitly rely on the hypothesis of statistical independence among the entries of the sensing matrix. Perhaps surprisingly, the method outperforms uniformly all the other state-ofthe-art methods in our tests.

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