Study on Piecewise Smooth Signal Reconstruction Algorithms based on Compressed Sensing

摘要

In this paper, the unknown piecewise smooth signal was chosen as tested signal. After random matrix were chosen as measure matrix, we design the CS (Compressed Sensing) model for the unknown piecewise smooth signal. The signal was reconstructed using the OMP (Orthogonal Matching Pursuit) algorithm. The linear combination wavelet bases were proposed by the authors and were chosen as the sparse base in the CS model. The simulation results show that CS model by this paper can acquire the better approximation of the original signal.%W artykule opisano metod? rekonstrukcji sygna?u odcinkowo-g?adkiego, z wykorzystaniem algorytmu OMP. Dane uzyskane z modelu próbkowania oszcz?dnego (ang. Compressed Sensing) sygna?u, umieszczono w wygenerowanej losowo macierzy pomiarowej. W algorytmie próbkowania wykorzystano falkowe kombinacje liniowe. Wykazano, ?e zastosowany model próbkowania oszcz?dnego pozwala na lepsz? aproksymacj? sygna?u.