### Abstract

Estimation problems with bounded, uniformly distributed noise arise naturally in reconstruction problems from over complete linear expansions with subtractive dithered quantization. We present a simple recursive algorithm for such bounded-noise estimation problems. The mean-square error (MSE) of the algorithm is "almost" ο(1/n ^{2}), where n is the number of samples. This rate is faster than the ο(1/n) MSE obtained by standard recursive least squares estimation and is optimal to within a constant factor.

Original language | English (US) |
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Pages (from-to) | 457-464 |

Number of pages | 8 |

Journal | IEEE Transactions on Information Theory |

Volume | 47 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2001 |

### Fingerprint

### Keywords

- Consistent reconstruction
- Dithered quantization
- Frames
- Overcomplete representations
- Overdetermined linear equations

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Information Systems

### Cite this

*IEEE Transactions on Information Theory*,

*47*(1), 457-464. https://doi.org/10.1109/18.904562

**Recursive consistent estimation with bounded noise.** / Rangan, Sundeep; Goyal, Vivek K.

Research output: Contribution to journal › Article

*IEEE Transactions on Information Theory*, vol. 47, no. 1, pp. 457-464. https://doi.org/10.1109/18.904562

}

TY - JOUR

T1 - Recursive consistent estimation with bounded noise

AU - Rangan, Sundeep

AU - Goyal, Vivek K.

PY - 2001/1

Y1 - 2001/1

N2 - Estimation problems with bounded, uniformly distributed noise arise naturally in reconstruction problems from over complete linear expansions with subtractive dithered quantization. We present a simple recursive algorithm for such bounded-noise estimation problems. The mean-square error (MSE) of the algorithm is "almost" ο(1/n 2), where n is the number of samples. This rate is faster than the ο(1/n) MSE obtained by standard recursive least squares estimation and is optimal to within a constant factor.

AB - Estimation problems with bounded, uniformly distributed noise arise naturally in reconstruction problems from over complete linear expansions with subtractive dithered quantization. We present a simple recursive algorithm for such bounded-noise estimation problems. The mean-square error (MSE) of the algorithm is "almost" ο(1/n 2), where n is the number of samples. This rate is faster than the ο(1/n) MSE obtained by standard recursive least squares estimation and is optimal to within a constant factor.

KW - Consistent reconstruction

KW - Dithered quantization

KW - Frames

KW - Overcomplete representations

KW - Overdetermined linear equations

UR - http://www.scopus.com/inward/record.url?scp=0035089196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035089196&partnerID=8YFLogxK

U2 - 10.1109/18.904562

DO - 10.1109/18.904562

M3 - Article

AN - SCOPUS:0035089196

VL - 47

SP - 457

EP - 464

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 1

ER -