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| Tekijä: | Ejaz, Aqib |
| Työn nimi: | Algorithms for Sparse Signal Recovery in Compressed Sensing |
| Julkaisutyyppi: | Diplomityö |
| Julkaisuvuosi: | 2015 |
| Sivut: | 9 + 65 Kieli: eng |
| Koulu/Laitos/Osasto: | Sähkötekniikan korkeakoulu |
| Oppiaine: | Signal Processing (S3013) |
| Valvoja: | Koivunen, Visa |
| Ohjaaja: | Ollila, Esa |
| Elektroninen julkaisu: | http://urn.fi/URN:NBN:fi:aalto-201506303499 |
| Sijainti: | P1 Ark Aalto 2962 | Arkisto |
| Avainsanat: | compressed sensing sparse modeling greedy algorithms MMSE Bayesian multichannel sparse recovery |
| Tiivistelmä (eng): | Compressed sensing and sparse signal modeling have attracted considerable research interest in recent years. The basic idea of compressed sensing is that by exploiting the sparsity of a signal one can accurately represent the signal using fewer samples than those required with traditional sampling. This thesis reviews the fundamental theoretical results in compressed sensing regarding the required number of measurements and the structure of the measurement system. The main focus of this thesis is on algorithms that accurately recover the original sparse signal from its compressed set of measurements. A number of greedy algorithms for sparse signal recovery are reviewed and numerically evaluated. Convergence properties and error bounds of some of these algorithms are also reviewed. The greedy approach to sparse signal recovery is further extended to multichannel sparse signal model. A widely-used non-Bayesian greedy algorithm for the joint recovery of multichannel sparse signals is reviewed. In cases where accurate prior information about the unknown sparse signals is available, Bayesian estimators are expected to outperform non-Bayesian estimators. A Bayesian minimum mean-squared error (MMSE) estimator of the multichannel sparse signals with Gaussian prior is derived in closed-form. Since computing the exact MMSE estimator is infeasible due to its combinatorial complexity, a novel algorithm for approximating the multichannel MMSE estimator is developed in this thesis. In comparison to the widely-used non-Bayesian algorithm, the developed Bayesian algorithm shows better performance in terms of mean-squared error and probability of exact support recovery. The algorithm is applied to direction-of-arrival estimation with sensor arrays and image denoising, and is shown to provide accurate results in these applications. |
| ED: | 2015-08-16 |
INSSI tietueen numero: 51907
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