Tsallis entropy penalized robust 1-bit compressive sensing against sign flips

One-bit compressive sensing (1BCS) has emerged as a prominent research area owing to its unparalleled advantages in sampling efficiency and hardware implementability of signal reconstruction. However, existing 1BCS methodologies encounter challenges of mitigating sign-flip noise and depending on prior knowledge of signal sparsity or noise level. To address these limitations, we propose a novel method named robust generalized fixed-point continuation via Tsallis entropy (RGFPC-TE). RGFPC integrates the fixed-point continuation (FPC) framework with an adaptive sign-flip detection mechanism. This integration enables the algorithm to iteratively refine measurements and recover the original signal without requiring prior of sparsity or noise level. Moreover, we theoretically prove that incorporating TE into the FPC framework enhances signal sparsity and energy concentration. Numerical experiments on synthetic signals and real images demonstrate the superiority of RGFPC-TE. In real-image reconstruction tasks, our method achieves up to 5 dB higher peak signal-to-noise ratio (PSNR) than state-of-the-art 1BCS algorithms.