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In this paper, we propose an adaptive compressed sensing scheme that utilizes a support estimate to focus the measurements on the large valued coefficients of a compressible signal. We embed a “sparse-filtering” stage into the measurement matrix by weighting down the contribution of signal coefficients that are outside the support estimate. We present an application which can benefit from the proposed sampling scheme, namely, video compressive acquisition. We demonstrate that our proposed adaptive CS scheme results in a significant improvement in reconstruction quality compared with standard CS as well as adaptive recovery using weighted ℓ1 minimization.