In the passive bistatic radar (PBR) system, methods exist to address the issue of detecting weak targets without being influenced by non-ideal factors from adjacent strong targets. These methods utilize the sparsity in the delay-Doppler domain of the cross ambiguity function (CAF) to detect weak targets. However, the modeling and solving of this method involve substantial memory consumption and computational complexity. To address these challenges, this paper establishes a target detection model for PBR based on batch processing of sparse representation and recovery. This model partitions the CAF into blocks, identifies blocks requiring processing based on the presence of targets, and improves the construction and utilization of the measurement matrix. This results in a reduction in the computational complexity and memory resource requirements for sparse representation and recovery, and provides favorable conditions for parallel execution of the algorithm. Experimental results indicate that the proposed approach increases the number of blocks by a factor of four, and reduces the number of real multiplications by approximately an order of magnitude. Hence, compared with the traditional approach, the proposed approach enables fast and stable detection of weak targets.