A kind of adaptive filter based on a new sparsity measure function

We propose a new sparsity measure function which effectively reflects the vector sparsity. Using the correspondingly developed Iterative Shrinkage/Thresholding Algorithms (ISTA) in filter´s adaptation process, our algorithm reduces the impact of measurement noise on the filter performance and converges accurately to the sparse solution. We also apply the Barzilai-Borwein (BB) method, which is developed for determinate environments, to calculate the step-size of adaptive filters with random input. The validity of BB method in adaptive filters is verified by its fast convergence rate in our tests. The idea of our method can actually be applied to general adaptive filters in sparse environments with performance improvements. Numerical simulations prove the effectiveness of the method: sparsity based adaptive algorithms achieve lower mean square error than original algorithms without sacrificing convergence rate.