Reference-based compressed sensing: A sample complexity approach

Abstract

We address the problem of reference-based compressed sensing: reconstruct a sparse signal from few linear measurements using as prior information a reference signal, a signal similar to the signal we want to reconstruct. Access to reference signals arises in applications such as medical imaging, e.g., through prior images of the same patient, and compressive video, where previously reconstructed frames can be used as reference. Our goal is to use the reference signal to reduce the number of required measurements for reconstruction. We achieve this via a reweighted 1-1 minimization scheme that updates its weights based on a sample complexity bound. The scheme is simple, intuitive and, as our experiments show, outperforms prior algorithms, including reweighted 1 minimization, 1-1 minimization, and modified CS.

Internet-of-Things data aggregation using compressed sensing with side information

“…The CS theory can be modified so as to leverage a signal correlated to the signal of interest, called side information (SI), which is assumed to be provided a priori at the decoder in order to aid reconstruction [15], [16], [22]- [26]. In particular, the decoder aims at recovering the signal x based on the measurements y, the measurement matrix A and a side information vector, say w, which is correlated with s. The problem of CS with side information can be expressed via the following 1 − 1 optimization problem [15], [16], [24]…”

Reference‐based MRI

“…In recent work, we have extended their theoretical analysis to our setting. 50 In particular, we developed a bound on the number of measurements required for perfect reconstruction of x with high probability in the presence of a reference. We also show that adding weights highly improves the results in comparison to other nonweighted ℓ 1 -minimization based solutions.…”

Bayesian Compressed Sensing with Heterogeneous Side Information

“…Hence, the estimation error was recovered instead of the sparse signal. The problem of CS with prior information was studied in [15][16][17], where, through bounds and geometrical interpretations, it was shown that 1 -1 minimization improves the performance of CS if the SI is of good enough quality.…”