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Rasika Kamble,
Shweta Ghadage,
Sayali Ghatule,
Vaibhav Godase,
- UG Student, Department of Electronics and Telecommunication Engineering, SKN Sinhgad College of Engineering, Pandharpur, Maharashtra, India
- UG Student, Department of Electronics and Telecommunication Engineering, SKN Sinhgad College of Engineering, Pandharpur, Maharashtra, India
- UG Student, Department of Electronics and Telecommunication Engineering, SKN Sinhgad College of Engineering, Pandharpur, Maharashtra, India
- Assistant Professor, Department of Electronics and Telecommunication Engineering, SKN Sinhgad College of Engineering, Pandharpur, Maharashtra, India
Abstract
High-resolution signal acquisition can require substantial sampling, storage, power, and transmission resources. Compressed sensing (CS) offers an alternative to conventional acquisition by exploiting sparsity or compressibility in a suitable representation to recover a signal from fewer linear measurements than its ambient dimension. This paper presents the mathematical foundations and a reproducible simulation study of sparse reconstruction for efficient signal acquisition. A one-dimensional signal of length 256 is generated with 12 non-zero coefficients in an orthonormal discrete-cosine-transform (DCT) representation. Random Gaussian measurement operators are used to acquire subsets of linear measurements, and an ℓ₁-regularized least-squares solver reconstructs the sparse coefficients. Reconstruction quality is assessed using normalized mean-square error (NMSE) across sampling ratios and additive measurement-noise levels. In a representative 96-measurement trial, the ℓ₁ reconstruction achieves an NMSE of approximately 0.0062, compared with approximately 0.648 for a minimum-norm least-squares reconstruction from the same underdetermined measurements. In repeated synthetic trials, the best mean NMSE occurs around a 30% sampling ratio for the selected sparsity and solver settings; error increases at the highest tested noise level. These results are specific to the constructed signal model, random measurement matrices, and regularization choices. The paper also discusses measurement design, algorithm selection, hardware considerations, and applications in biomedical imaging, communications, radar, remote sensing, and sensor networks. The central conclusion is that CS can reduce measurement counts when sparsity and measurement incoherence are credible, but acquisition savings must be balanced against reconstruction cost, noise, model mismatch, and the risk of losing non- sparse information.
Keywords: Compressed Sensing; Compressive Sampling; Sparse Reconstruction; Signal Acquisition; Normalized Mean-Square Error.
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Current Trends in Signal Processing
| Volume | 16 | |
| 03 | ||
| Received | 19/10/2026 | |
| Accepted | 25/10/2026 | |
| Published | 04/11/2026 | |
| Publication Time | 16 Days |