2019/09/16 by Daws, Joseph, Petrosyan, Armenak, Tran, Hoang +1
#65D99 #FOS: Electrical engineering #FOS: Mathematics #I.4.5 #Image and Video Processing (eess.IV) #Numerical Analysis (math.NA) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1909.07270
In this effort, we propose a convex optimization approach based on weighted ℓ1-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the wavelet coefficients associated to the functional representation of the object of interest by solving our proposed optimization problem. We give a specific choice of weights and show numerically that the chosen weights admit efficient recovery of objects of interest from either a set of sub-samples or a noisy version. Our method not only exploits sparsity but also helps promote a particular kind of structured sparsity often exhibited by many signals and images. Furthermore, we illustrate the effectiveness of the proposed convex optimization problem by providing numerical examples using both orthonormal wavelets and a frame of wavelets. We also provide an adaptive choice of weights which is a modification of the iteratively reweighted ℓ1-minimization method.