A Stochastic Multirate Signal Processing Approach to High-Resolution Signal Reconstruction

Abstract

The paper addresses the problem of reconstructing a signal at some high sampling rate from a set of signals sampled at a lower rate and subject to additive noise and distortion. A set of periodically time-varying filters are employed in reconstructing the underlying signal. Results are presented for a one-dimensional case involving simulated data, as well as for a two-dimensional case involving real image data where the image is processed by rows. In both cases, considerable improvement is evident after the processing.

Statistical Multirate High-Resolution Signal Reconstruction Using the EMD-IT Based Denoising Approach

“…For a reliable evaluation, the results obtained by the proposed method are also compared to those of method [7]. Since the LR signals are maximally decimated (downsampled) forms of the considered HR signals, the decimation factor is L i = L = 3 and the number of Wiener filter coefficients required in [7] is taken as P = 8.…”

“…One of the existing methods to solve the problem emphasized above employs linear periodically time-varying (LPTV) Wiener filters that are optimal in mean-squares sense [7]. As shown in Fig.…”

“…Within the scope of the reconstruction or estimation of a WSS random signal through its noisy LR measurements observed at different sampling rates, studies that employ the optimal linear filtering referred as Wiener filtering are carried out under the guidance of Therrien [3][4][5][6][7][8][9]. The problem of estimating a WSS random signal from two sequences observed separately at full-rate and half-rate, and both of which are affected by measurement noise is investigated in [3].…”

“…A generalized version of [3] is considered in [5] that is a preliminary work of dissertation presented in [6] where optimal multirate filtering procedure is formulated taking the second-order statistics into consideration for the goal of estimating an HR signal from LR measurements observed at different sampling rates. In [7], derivations in [5] and [6] are adapted to reconstruct an HR signal from a set of its noisy and distorted LR versions. Eventually, on the basis of the LS approach, formulations of multirate optimal filtering derived in [5][6][7] are extended to the two-dimensional case [8] (refer to [9] for detailed information).…”

“…In [7], derivations in [5] and [6] are adapted to reconstruct an HR signal from a set of its noisy and distorted LR versions. Eventually, on the basis of the LS approach, formulations of multirate optimal filtering derived in [5][6][7] are extended to the two-dimensional case [8] (refer to [9] for detailed information). It is remarked that both ME and Wiener filter based methods require the knowledge of second-order statistics related to the desired HR signal and the noisy LR observations.…”