BPDQ$_{p}$-Net: A Deep Unfolding Method for Quantized Compressed Sensing

As a classic quantization compressed sensing method, the Basis Pursuit DeQuantizer of moment
$p$
(BPDQ
$_{p}$
) theoretically shows that compared to
$\ell _{2}$
norm,
$\ell _{p}$
norm (
$p > 2$
) can more faithfully model quantization distortion and its performance improves with larger
$p$
. However, as the
$p$
increases, the computational complexity of the algorithm increases sharply, which undoubtedly greatly limits the application of BPDQ
$_{p}$
in practical scenarios. Moreover, limited by manual parameter fine-tuning, the performance of the algorithm is also difficult to fully release. To solve these problems, we design a modified BPDQ
$_{p}$
, and by mapping its solving process into a neural network structure, we further propose a deep unfolding model, named BPDQ
$_{p}$
-Net, whose network architecture does not change with
$p$
. Since all model parameters can be optimized and updated with training data, the proposed model can accurately and efficiently reconstruct quantization signals. Our simulation results show that compared with BPDQ
$_{p}$
, the proposed BPDQ
$_{p}$
-Net improves the signal reconstruction speed by three orders of magnitude and the reconstruction accuracy by about 50%.