Robustness of compressive Fourier-domain sampling against rounding-off errors and noise

Abstract

We investigate the robustness of compressive Fourier-domain sampling against the effect of rounding-off errors and ambient noise. Compressive sampling (CS) is accomplished with a two-dimensional line mask that samples the low frequency components of a signal at the prescribed Nyquist rate while undersampling its associated highfrequency components. Generally, the signal energy and details are encoded mostly in the low and high-frequency components, respectively. Rounding-off errors arise when an analog signal is digitized with an n-bit analog-to digital converter (ADC) that limits the dynamic range of the digital-signal amplitude representation to 2ⁿ different possible values. We show that reducing the dynamic range from ADC bit-number n = 64 to n = 14, does not compromise the CS reconstruction performance even at an effective sampling rates that is only a fraction (1/10, 1/5 and 3/10) of the Nyquist rate in the presence of additive Fourier domain noise. Lowering the dynamic range from n = 14 to n = 1 produces a reconstruction error that increases linearly with decreasing n. This behavior is observed for different images and noise strengths.