Compressive Imaging Using Frequency Spectrum Coding

In traditional signal sampling process, Shannon-Nyquist (Shoon-Nyquist) samplingtheorem is a fundamental principle that must be followed, in that the sampling frequencymust be at least twice the highest frequency of the sampled signal. However, with theincreasing of data acquisition capabilities of sensing systems, acquisition ofhigh-resolution images will inevitably lead to a flood of sampling data according toShoon-Nyquist sampling theorem, which increases the cost of data transport and storage,and also the demand for the resolution of the detector. Donoho and Candes proposed thecompressed sensing theory which is considered as a revolutionary breakthrough in that itbreaks Shoon-Nyquist sampling frequency requirements. For compressible or sparsesignals, signal sampling can be implemented with the sampling frequency that is less thanthat of Shoon-Nyquist sampling theorem, and the signal is also compressed meanwhile.In this thesis, based on the theory of the compressed sensing, a compression imagingmode was studied by coding the frequency spectrum plane of an optical Fourier transformsystem. With appropriate algorithm for the image reconstruction, high-resolution imagescan be achieved with the use of low-resolution detectors, and the required data storagespace is reduced. The characteristics of the proposed imaging mode are investigated withnumerical simulation. Simulation results show that high quality images can bereconstructed with data that is far less than that of original signal, which demonstrates thefeasibility of the proposed compression coding on the frequency spectrum plane. Incomparison to the conventional compressed sensing technique, real-time compression canbe achieved with the proposed method.The thesis also studied compressive coding imaging based on optical wavelet transform coupled with the frequency spectrum coding. The imaging quality can beenhanced by introducing optical wavelet transform for pre-treatment of the target imagebefore the compression coding on the frequency spectrum plane. Simulation results showthat higher quality images can be obtained with the pre-treatment of optical wavelettransform than that of purely optical Fourier transform without any increasing of thetransmitted data.