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The existing lensless compressive camera (L2C2) [1] suffers from low capture rates, resulting in low resolution images when acquired over a short time. In this work, we propose a new regime to mitigate these drawbacks. We replace the global-based compressive sensing used in the existing L2C2 by the local block (patch) based compressive sensing. We use a single sensor for each block, rather than for the entire image, thus forming a multiple but spatially parallel sensor L2C2.