Recovery of signals from non-uniform samples: An application to wireless sensor networks
Wireless sensor networks attracted researchers for the unique challenges and the opportunities in signal processing. In applications involving environmental monitoring, sensors are not placed regularly, they are placed irregularly depending on the application. Reconstruction of the fields from sensors placed non-uniformly is of interest. The Optimal Recovery (OR) approach is used for reconstructing the fields from non-uniform samples. The OR method is first applied to one dimensional signals and then this approach is extended to two dimensional signals. The basic step in OR approach is to find the minimum norm signal that interpolates the given samples. In wireless sensor networks, fields of interest are obtained on irregular sampling grids. Reconstruction of the irregularly spaced fields can be done using cubic spline interpolation. Spline methods do not allow the parameter bandwidth to be incorporated in the interpolation which is the drawback over the OR method. Signals can be reconstructed using OR method in two ways: from samples placed uniformly and from samples placed non-uniformly. Reconstruction of the fields from non-uniform samples is the main topic of this thesis. Sensor measurements in a field are divided into non-overlapping clusters or blocks. Two types of reconstructions are possible in reconstructing the signal: using a single block (cluster) and using block-by-block. In reconstruction using single block, information of a single cluster is used to reconstruct the signal with in the block and beyond the block. In block by block approach sensor measurements are divided into non-overlapping blocks and the field is reconstructed local to each block only. In reality, sensor location values may not be correctly determined. There may be some deviation from the exact values. Even a small change in location can result in large changes in the reconstructed signal. This problem is addressed with a regularization parameter that de-sensitizes the constraint imposed by the given samples in OR. In some cases the data values can also be corrupted due to noise. The effects of errors on sensor locations and errors on data values are analyzed and rectified using the regularization parameter in OR approach.
Upadhyayula, Lata Neelima, "Recovery of signals from non-uniform samples: An application to wireless sensor networks" (2008). ETD Collection for University of Texas, El Paso. AAI1456745.