Selective Visual Attention: Computational Models and Applications

8.5 Application in Compressive Sampling

In image and signal coding, an analogue signal or image is first transferred to digital data by sampling. The conventional approach of sampling signals or images follows Shannon's theorem: the sampling rate must be at least two times the maximum frequency (Nyquist frequency) present in the signal or image. For a high-resolution image with higher maximum frequency, the sampling data often includes huge numbers of pixels (billions or even trillions of pixels). The digital image has to be compressed by image coding for storage or transmission, and then the original digital image is recovered in the decoding stage. In the general image compression algorithm, as mentioned in Section 8.3, a digital image is first transformed into an appropriate basis space such as a discrete Fourier transform, a discrete cosine transform, a wavelet transform and so on, then only a few important coefficients in the transform domain are used to encode the information, and many other coefficients are discarded during this encoding process, so that the data of the image is compressed. In the decoding stage, the original digital image can be recovered based on a few important coefficients. In fact, much information obtained at the sampling stage is wasted in the process of image encoding and decoding. Is there a method that can find fewer data in the sampling stage? The original digital image can then be recovered from the obtained partial data.

A recent study has shown ...