Ridge Regression and Iterative Hard-Thresholding Guided Interpolation from Noisy Samples by Prolate Spheroidal Wave Functions

Interpolation aims to retrieve missing values. Resulting from the inaccuracy of sensors, channel distortion, and a variety of measurement errors, signals are contaminated with noise. To well interpolate these noisy signals, an adaptive interpolation algorithm is proposed in this work. First, a novel atom selection mechanism, which incorporates the ridge regression problem and the iterative hard-thresholding algorithm, is applied to identify dominant frequencies. The essential time-frequency information is thus precisely extracted. Prolate spheroidal wave functions, which are highly concentrated in the time-frequency plane, are then appropriately modulated. Finally, atoms are refined to form a proper basis dictionary for signal expansion and interpolation. Comprehensive experiments are conducted to validate that the proposed RidIHT algorithm has outstanding performance in interpolating from noisy samples.