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.