Study On Fast Fixed Point Algorithm And Its Application Based On Compressed Sensing

There’s a larger ascension space for the signal reconstruction speed and quality of iteration algorithms. Fixed point continuation(FPC) algorithm is a kind of soft(shrinkage) thresholding method. And this paper gives the systematic research of convergence speed and reconstruction precision of it. There’re three innovations of this paper, which are introduced as the following:In the first part of innovations is a fast fixed point continuation(FFPC) algorithm. Based on FPC algorithm, FFPC introduces a step parameterkt, combines the two contiguous iteration results with 11kktt+-and sets the combination result as the input point of next iteration. Besides, FFPC uses a shrinkage factor b to reduce the regularized paprameter m. The mathematical analysis proves that the convergence speed of FFPC algorithm is faster than FPC. Further more, compared to other algeithms, the simulations for one-dimensional signal and image signals get better results at both reconstruction speed and quality.The second part proposes a fast fixed point continuation_ active set algorithm, which adds a subspace optimization stage of FPC algorithm to get more accurate solutions by making full use of greedy and convex optimization algorithms in compreesed sensing. FFPC_AS algorithm executes the shrinkage stage and the subspace optimization stage alternatively which makes better performance without carrying out debiase operation. This part gives the alternate implementation scheme and its convergence proof. The experimental results show the superior property of FFPC_AS algortithm more directly, such as, it can raise the speed and accuracy for reconstructing image signals.The third part proposes a stage-of-art algorithm named block fixed point contimuation_active set, which applies the block compressed sensing theory to FFPC_AS algorithm and presents a partion strategy of two kinds of signals based on block sampling and structured compressed sensing theory. In coding side, uses this strategy to execute signal sampling. And at the decoding side, uses fast coordinate drop(BCD) technology to reconstruct the signal piece by piece, and then join the activities of each block piece together according to the original signal structure and takes subspace optimization operation at last. BFFPC_AS algorithm not only improves the quality of the signal reconstruction, but also effectively eliminates the block effect of traditional block reconstruction. The simulation experimental results show that the image signal reconstruction by BFFPC_AS algorithm has the best visual effect with small reconstruction error and higher peak signal-to-noise ratio. When solves large-scale optimization problems, BFFPC_AS algorithm not only saves the storage and transmission space of measurement matrix, but also can quickly and accurately reconstructs the signal.