Invariancy of Sparse Recovery Algorithms

Kharratzadeh, Milad; Sharifnassab, Arsalan; Babaie‐Zadeh, Massoud

doi:10.1109/tit.2017.2686428

Cited by 5 publications

(4 citation statements)

References 47 publications

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“…The conditioning of the dictionary characterizes how different its atoms are [52]. The performance of a sparse recovery algorithm is affected by the conditioning.…”

Section: Mipmentioning

confidence: 99%

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Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics

Swamy

Wang

et al. 2023

Mathematics

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Compressed sensing is an alternative to Shannon/Nyquist sampling for acquiring sparse or compressible signals. Sparse coding represents a signal as a sparse linear combination of atoms, which are elementary signals derived from a predefined dictionary. Compressed sensing, sparse approximation, and dictionary learning are topics similar to sparse coding. Matrix completion is the process of recovering a data matrix from a subset of its entries, and it extends the principles of compressed sensing and sparse approximation. The nonnegative matrix factorization is a low-rank matrix factorization technique for nonnegative data. All of these low-rank matrix factorization techniques are unsupervised learning techniques, and can be used for data analysis tasks, such as dimension reduction, feature extraction, blind source separation, data compression, and knowledge discovery. In this paper, we survey a few emerging matrix factorization techniques that are receiving wide attention in machine learning, signal processing, and statistics. The treated topics are compressed sensing, dictionary learning, sparse representation, matrix completion and matrix recovery, nonnegative matrix factorization, the Nyström method, and CUR matrix decomposition in the machine learning framework. Some related topics, such as matrix factorization using metaheuristics or neurodynamics, are also introduced. A few topics are suggested for future investigation in this article.

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“…The conditioning of the dictionary characterizes how different its atoms are [52]. The performance of a sparse recovery algorithm is affected by the conditioning.…”

Section: Mipmentioning

confidence: 99%

“…Sparse recovery algorithms with invariance properties are less affected when the sensing matrix (i.e., the dictionary) is ill-conditioned [52]. There implicitly exists an equivalent well-conditioned problem.…”

Section: Sparse Recoverymentioning

confidence: 99%

Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics

Swamy

Wang

et al. 2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…Since the problem is LP0 type one, we start from b and then look for a column of A which is most correlated with it which gives the minimum dot product value as a reference for comparison. In accordance with [33], this algorithm is non-invariant under an illconditioned dictionary.…”

Section: Sparse Recovery Algorithmsmentioning

confidence: 99%

Compressed Sensing System for a Fingerprint Image Recognition Using Sensing Matrix with Chaotic Model-Based Deterministic Row Indexes

Hailemariam

Gupta

2021

Preprint

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This paper proposes a novel design approach for a secured compressed sensing system for fingerprint imaging and its transmission. In the proposed design, the first stage is acquiring the signal followed by sparsely modeling it using Orthogonal Matching Pursuit (OMP) algorithm. In addition to compressing, to guaranty its security, we multiply the sparse modeled data by a novel deterministic partially orthogonal Discrete Cosine Transform (DCT) sensing matrix. Furthermore, the construction of the sensing matrix uses a modified Multiplicative Linear Congruential Generator (MLCG) to select the row index appropriately from chaotically re-arranged rows of DCT pseudo-randomly. On the other hand, the simultaneous recovering and decryption of the compressed image accomplished with the help of a convex optimization method. The proposed system tested by employing different image and security assessment techniques. The results show that we have archived better Peak Signal to Noise Ratio (PSNR) than the recommended value for wireless transmission using samples below 25%.

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“…These systems, however, must always deal with sparse input signals. A sparse input signal can be recovered to its original form from few measured samples within a compressed samplingsbased signal processing system [7] [20]. It can be achieved by transformation of a high dimensional signal to a lower one through matrix multiplication once the actual measurements are available from the input [21].…”

Section: Introductionmentioning

confidence: 99%

Compressed sensing based fingerprint imaging system using a chaotic model-based deterministic sensing matrix

Hailemariam

Gupta

2022

Multimed Tools Appl

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A novel deterministic sensing matrix design approach applied to enable secured compressed sensing and transmission of fingerprint images. The performance of the sensing matrix was analyzed in detail by varying compressed sensing and security parameters. The number of sampling and sparse coefficient are the parameters taken under consideration from compressed sensing, whereas the encryption key is from the security scheme. The first stage in the performance study is acquiring the signal, and followed by sparsely modelling it using Orthogonal Matching Pursuit (OMP) algorithm. The sparse modelled data is multiplied by the proposed deterministic partial orthogonal Discrete Cosine Transform (DCT) sensing matrix to reduce its dimension and encrypt it. To introduce confusion on the DCT matrix rows, the pseudorandom permutation is applied to the DCT matrix rows before sensing matrix derivation. Additionally, recovering and decryption of the compressed image accomplished with the help of a convex optimization method. The results obtained from the simulation of the proposed system confirmed that a better Peak Signal to Noise Ratio (PSNR) than the recommended value for wireless transmission is archived using a sample below 25% without losing a significant number of fingerprint minutiae.

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Invariancy of Sparse Recovery Algorithms

Cited by 5 publications

References 47 publications

Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics

Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics

Compressed Sensing System for a Fingerprint Image Recognition Using Sensing Matrix with Chaotic Model-Based Deterministic Row Indexes

Compressed sensing based fingerprint imaging system using a chaotic model-based deterministic sensing matrix

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