A fast reconstruction algorithm for deterministic compressive sensing using second order reed-muller codes

Howard, Stephen D.; Calderbank, A.R.; Searle, Stephen J.

doi:10.1109/ciss.2008.4558486

Cited by 135 publications

(176 citation statements)

References 13 publications

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“…We emphasize that even when compared to its other sub-linear counterparts (e.g. [16][17][18][19], our algorithm has minimum storage requirement and relies on very rudimentary signal-processing techniques that do not rely on higher-order interaction of elements of y and Φ. …”

Section: Hypothetical Hardware Implementationmentioning

confidence: 99%

An analog sub-linear time sparse signal acquisition framework based on structured matrices

Yoo

Khajehnejad

Hassibi

et al. 2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Advances in compressed-sensing (CS) have sparked interest in designing information acquisition systems that process data at close to the information rate. Initial proposals for CS signal acquisition systems utilized random matrix ensembles in conjunction with convex relaxation based signal reconstruction algorithms. While providing universal performance bounds, random matrix based formulations present several practical problems due to: the difficulty in physically implementing key mathematical operations, and their dense representation. In this paper, we present a CS architecture which is based on a sub-linear time recovery algorithm (with minimum memory requirement) that exploits a novel structured matrix. This formulation allows the use of a reconstruction algorithm based on relatively simple computational primitives making it more amenable to implementation in a fully-integrated form. Theoretical recovery guarantees are discussed and a hypothetical physical CS decoder is described.

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Section: Hypothetical Hardware Implementationmentioning

confidence: 99%

An analog sub-linear time sparse signal acquisition framework based on structured matrices

Yoo

Khajehnejad

Hassibi

et al. 2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…The reconstruction algorithm is good for 1D signals but in experiments given in [15] the 1D signals are of size or 67 2 only, much smaller than the size encountered for 2D signals, such as images. 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.…”

Section: Introductionmentioning

confidence: 99%

“…They show that such deterministic sensing matrices sat-isfying StRIP can be constructed by chirps, Reed-Muller (RM) sequences, and BCH codes, as done in [15][16][17]. In the presence of noise, if Φ satisfies the StRIP property with parameters and δ, the reconstruction error due to the Quadratic Reconstruction Algorithm is given by…”

Section: Introductionmentioning

confidence: 99%

“…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]. The fast reconstruction algorithm [15][16][17] is called the Quadratic Reconstruction Algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…The advantage of using deterministic matrices for compressed sensing is that reconstruction can be very efficient [15,16]. The fast reconstruction algorithm [15][16][17] is called the Quadratic Reconstruction Algorithm. This algorithm takes advantage of the multivariable quadratic functions that appear as exponents of the entries in the sensing matrix, and therefore, only requires vector-vector multiplication instead of matrix-vector multiplication required in Basis and Matching Pursuit algorithms that are used for reconstructions with random sensing matrices.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Sparse Vector Coding for Ultra‐reliable and Low‐latency Communications

Shim

2023

Ultra‐Reliable and Low‐Latency Communications (URLLC) Theory and Practice

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A fast reconstruction algorithm for deterministic compressive sensing using second order reed-muller codes

Cited by 135 publications

References 13 publications

An analog sub-linear time sparse signal acquisition framework based on structured matrices

An analog sub-linear time sparse signal acquisition framework based on structured matrices

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

Sparse Vector Coding for Ultra‐reliable and Low‐latency Communications

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