The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Numerical analysis of the non-uniform sampling problem
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 vol. II: interpolation and extrapolation
Adaptive reference levels in a level-crossing analog-to-digital converter
EURASIP Journal on Advances in Signal Processing
EURASIP Journal on Advances in Signal Processing - Special issue on applications of time-frequency signal processing in wireless communications and bioengineering
Analysis and design of minimax-optimal interpolators
IEEE Transactions on Signal Processing
Nonuniform Interpolation of Noisy Signals Using Support Vector Machines
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
IEEE Transactions on Image Processing
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In this paper, we propose a method for efficient signal reconstruction from non-uniformly spaced samples collected using level-crossing sampling. Level-crossing (LC) sampling captures samples whenever the signal crosses predetermined quantization levels. Thus the LC sampling is a signal-dependent, non-uniform sampling method. Without restriction on the distribution of the sampling times, the signal reconstruction from non-uniform samples becomes ill-posed. Finite-support and nearly band-limited signals are well approximated in a low-dimensional subspace with prolate spheroidal wave functions (PSWF) also known as Slepian functions. These functions have finite support in time and maximum energy concentration within a given bandwidth and as such are very appropriate to obtain a projection of those signals. However, depending on the LC quantization levels, whenever the LC samples are highly non-uniformly spaced obtaining the projection coefficients requires a Tikhonov regularized Slepian reconstruction. The performance of the proposed method is illustrated using smooth, bursty and chirp signals. Our reconstruction results compare favorably with reconstruction from LC-sampled signals using compressive sampling techniques.