  We investigate the channel estimation (CE) problem for hybrid RIS assisted
systems and focus on the near-field (NF) regime. Different from their far-field
counterparts, NF channels possess a block-sparsity property, which is leveraged
in the two developed CE algorithms: (i) boundary estimation and sub-vector
recovery (BESVR) and (ii) linear total variation regularization (TVR). In
addition, we adopt the alternating direction method of multipliers to reduce
their computational complexity. Numerical results show that the linear TVR
algorithm outperforms the chosen baseline schemes in terms of normalized mean
square error in the high signal-to-noise ratio regime while the BESVR algorithm
achieves comparable performance to the baseline schemes but with the added
advantage of minimal CPU time.
