Keywords: Parallel Programming, optimization, l1 Abstract: We consider the recovery of signal via compressive sensing where the signal itself or its gradient are assumed to be sparse. This amounts to solve a l1 or a Total Variation minimization problem. We propose minimization algorithms specifically designed to take advantage of shared memory, vectorized, parallel and manycore microprocessors such as the Cell processor, new generation Graphics Processing Units (GPUs) and standard vectorized multicore processors (e.g. standard quad core CPUs).