Platelet is a multiscale representation developed for Poisson noise-removal from images. The existing platelet denoising algorithm requires O( N4) computations for an N×N image. In this paper, we introduce geometric platelet algorithm, which has a reduced computational complexity of O(N3logN). In the platelet algorithm, the exhaustive search required to compute an optimal platelet representation of the image is the major contributing factor to its computational requirements. In the proposed algorithm, this step is made faster by first learning the local geometry of the image by using Lucas-Kanade gradient descent algorithm. This geometric information is used to reduce the number of required searches, thereby reducing the run-time of the algorithm. We further extend the geometric platelet algorithm to include quadlet atoms, constructed from second-order bivariate polynomials. We validate the performance of the proposed algorithms by applying them on the simulated as well as real-world Poisson noisy images. © 2013 Elsevier B.V.