Motivated by recent results on compressed sensing cameras we consider cameras that perform an analog linear transformation Φ on the signal, followed by scalar quantization. Specifically we ask: is it better to use compressed sensing (Φ is an under-sampling random matrix) or direct sensing (Φ is the sparsifying basis)? We compare the two approaches using their energy-distortion tradeoffs: assuming most of the energy consumed by such systems is in the ADC and the energy of the quantizer doubles with each bit, which system will give lower distortion for the same energy consumption? We present analytic expressions for the energy-distortion curves for three signal models: signals residing in a known subspace, sparse signals and power-law signals. For all of these models, our analysis shows that direct sensing results in lower distortion for a given energy consumption. We also present simulation results for natural images showing that direct sensing of Haar wavelet coefficients is preferable for these signals. Given the assumptions of our model, direct sensing of Haar wavelets can achieve high quality imaging (PSNR of 40 dB) with 6% the power consumption of standard cameras using 8 bits per channel.
Year of publication
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, 36-44