A novel iterative method for the reconstruction of signal from nonuniformly spaced samples

A Versatile Iterative Framework for the Reconstruction of Bandlimited Signals from Their Nonuniform Samples

“…The usefulness of the proposed framework is demonstrated by studying in detail an efficient iterative method called Richardson iteration (RI) [13]. Unlike the block-based iterative methods in [9][10][11], the proposed iterative method can be realized in a sample-by-sample manner so as to further reduce computational costs. Moreover, the proposed framework provides a general form for solving the reconstruction problem using iterative methods, which greatly extends the previous works in [9][10][11].…”

“…Unlike the block-based iterative methods in [9][10][11], the proposed iterative method can be realized in a sample-by-sample manner so as to further reduce computational costs. Moreover, the proposed framework provides a general form for solving the reconstruction problem using iterative methods, which greatly extends the previous works in [9][10][11]. Based on this framework, extension to other iterative methods such as Jacobi iteration, Gauss-Seidel iteration and successive over relaxation algorithms is also possible.…”

“…As will be illustrated in Section 3, this problem can generally be viewed as solving a system of linear equations with infinite dimension. An important difference between the proposed approach and conventional iterative methods in [9][10][11] using the truncated sinc series is that the ideal response is only approximated in the frequency range of interest, i.e. the signal bandwidth.…”

“…In general cases where the sampling pattern is nonperiodic, the filter bank structure cannot be applied directly, as it is only applicable to the periodic sampling case with fixed timing mismatch. Iterative methods such as [9][10][11] were commonly used for the recovery of nonperiodically sampled signals. However, the implementation complexities of these approaches are generally higher than those of filter banks because of its iterative nature and large number of multiplications involving all or a large batch of samples in order to achieve high reconstruction accuracy.…”

“…In [9][10][11], the infinite sinc series are truncated directly to approximate the ideal fractional delay operation in (3). However, due to the slow decay of the sinc function, the truncation error for the approximation would be substantial.…”