Ressearch And Application For Compressive Sensing On Image Processing

As traditional sampling principle, the Nyquist sampling theorem indicates that the signal canbe reconstructed correctly under the condition that the sampling rate should exceed or equatedouble of the bandwidth of signal. Otherwise, there will be aliased distortion. It is the basis in thefield of information theory, especially signal and image processing. In some applications,however, the sampling theorem requires very high sampling rate which is difficult and expensiveto realize in hardware. In addition, it is also time-consuming for enormous data, such as MRI,CT, SAR image and so forth. For another, much resources will be used in the procedure ofsignals and images transmission (sample->store->compress->transmit), such as mathematicaloperation and memory. And the efficiency of this procedure is low.Recently, a novel sensing/sampling strategy called compressive sensing(CS), has greatlyattracted peoples' interest, for it breaks though the limitation of Nyquist sampling theorem. Itasserts that it captures and represents the sparse signals or images at a rate significantly belowthe Nyquist rate and they can be reconstructed "perfectly". This paper discusses the applicationof compressive sensing in signal and image processing, and the main contributions of this paperare as follows:(1) Researched compressive sensing theory and geometrical grouplets. Discussed sparserepresentation in different transform spaces, including fourier transform, wavelet transformand grouplet transform. Furthermore, introduced two types of reconstruction algorithmscalled Orthogonal Matching Pursuit(OMP) and Gradient Projection for SparseReconstruction(GPSR).(2) Proposed a new method about compressive sensing based on grouplet, which can takeadvantage of geometrical image regularities according to flexible multiscale associationfield. And represented images sparsely in the grouplet transform space. The experimentsresults demonstrated the effectiveness of method. For comparison, meanwhile, therepresentations in the wavelet transform space were given too.(3) At last, expand the application of CS. Applied compressive sensing to ultrasonic medicineimage. Took structurally random matrices(SRM) as measurement matrices and represented the image sparsely in the wavelet transform space. Finally, utilized GPSR to reconstruct theimage. The experiments showed that it was reasonable to apply compressive sensing toultrasonic medicine image, and the images could be reconstructed well.