| Summary: | 碩士 === 國立清華大學 === 通訊工程研究所 === 102 === Compressive sensing (CS), a new mathematical theory for sampling and compression, has drawn quite much attention since it was proposed in 2004. It tells that a signal can be reconstructed accurately using a small number (much less than suggested by Nyquist rate) of nonadaptive linear projections of this signal, as long as it exhibits sparsity in some domain: the most coefficients under some orthogonal basis are zero or near-zero.
In this thesis, we make a brief introduction to CS theory and various algorithms solving this problem, such as linear programming (LP), belief propagation (BP) and so on. Then we propose a CS scheme to sense and recover natural images, which can be applied to the single-pixel digital camera. The basic idea of this framework is sensing and recovering column by column, in a progressive way, for the sake of reducing the size of sensing matrix and recovering complexity. As the fact that the columns of a natural image have different sparsity, we take a “folding” action to make the sparsity of each column approximately equal when sensing. At the recovering processing, we employ iteratively cooperative reconstructions based on a hybrid transform maintaining the local smoothness and introduce $3$D transform-domain collaborative filtering based on non-local means (NLM), remaining the nonlocal self-similarity of natural images.
With the help of Matlab package CVX, the results say that the iteratively cooperative reconstruction has a gain of $4\sim 5$ dB on PSNR. Also, the recovery strategy we proposed has low complexity but maintaining good quality both on PSNR and visual sense. The value of PNSR is a little better than which recovering the whole image once, but the computing time is less than it.
Furthermore, in order to reduce the computational time, we proposed a novel algorithm based on belief propagation (BP), which quickly solved the problem above.
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