Reconstruction of the sequence of Diracs from noisy samples via maximum likelihood estimation
- Resource Type
- Conference
- Authors
- Hirabayashi, Akira; Iwami, Takuya; Maeda, Shuji; Hironaga, Yosuke
- Source
- 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on. :3805-3808 Mar, 2012
- Subject
- Signal Processing and Analysis
Communication, Networking and Broadcast Technologies
Components, Circuits, Devices and Systems
Computing and Processing
Noise measurement
Vectors
Signal to noise ratio
Maximum likelihood estimation
Probability density function
Technological innovation
Sequence of Diracs
signals with finite rate of innovation
annihilating filter
maximum likelihood estimation
- Language
- ISSN
- 1520-6149
2379-190X
We propose a reconstruction procedure for periodic sequence of K Diracs from noisy uniform measurements based on the maximum likelihood estimation. We first express the noise vector using the measurement vector and estimation parameters. This expression and the probability density function (PDF) for the noise vector allow us to define the (log-) likelihood function. We show that when the PDF is Gaussian, the maximization of the likelihood function is equivalent to finding the nearest sequence to the noisy sequence in the Fourier domain. This problem can be efficiently solved by combining an analytic solution and the so-called particle swarm optimization (PSO) search. Computer simulations show that the proposed method outperforms the conventional methods with computational cost of approximately O(K).