Achieving Super-Resolution With Redundant Sensing

Abstract

Analog-to-digital (quantization) and digital-toanalog (de-quantization) conversion are fundamental operations of many information processing systems. In practice, the precision of these operations is always bounded, first by the random mismatch error (ME) occurred during system implementation, and subsequently by the intrinsic quantization error (QE) determined by the system architecture itself. In this manuscript, we present a new mathematical interpretation of the previously proposed redundant sensing (RS) architecture that not only suppresses ME but also allows achieving an effective resolution exceeding the system's intrinsic resolution, i.e. super-resolution (SR). SR is enabled by an endogenous property of redundant structures regarded as "code diffusion" where the references' value spreads into the neighbor sample space as a result of ME. The proposed concept opens the possibility for a wide range of applications in low-power fully-integrated sensors and devices where the costaccuracy trade-off is inevitable.

MRI-Based Image Signal-to-Noise Ratio Enhancement with Different Receiving Gains in K-Space

“…Signal acquisition research has thus far focused on the maximum signal-to-noise ratio (SNR) at individual amplitude points to prevent saturation under a fixed receiving gain (RG). Several researchers have attempted to improve the SNR by reducing the receiver noise [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ]. When compared with analog receivers, digital receivers can reduce the noise of nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI), thereby improving the SNR [ 1 , 2 , 3 , 4 ].…”

“…However, their proposed superconducting ADC requires ultra-low temperatures to function, which limits its practical application in MRI. Diu and A.T. used redundant information detection to achieve a lower sampling noise and a higher sampling resolution for the internal design of an ADC, further improving the quantization SNR [ 7 , 8 ]. However, because this method involves chip design, its implementation is more complex.…”

“…Because the amplitude of the free induction decay (FID) signal of NMR fluctuates greatly in terms of duration, the method for reducing the receiver noise under a fixed RG proposed in the literature [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ] leverages the entire resolution of an ADC for the part with a larger amplitude in the signal; however, it does not consider the dynamic range of the signal across the entire period during the quantization process. Although measures have been taken to reduce the sampling noise, the parts of the signal with smaller amplitudes still cannot leverage the full resolution of an ADC [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 11 ], meaning that the maximum possible SNR cannot be achieved. In 2011, Takeda et al proposed a solution, namely, Apodization after Receiver Gain Increment during Ongoing Sequence with Time (APRICOT).…”