We propose a sparse imaging methodology called chaotic sensing (ChaoS) that enables the use of limited yet deterministic linear measurements through fractal sampling. A novel fractal in the discrete Fourier transform is introduced that always results in the artifacts being turbulent in nature. These chaotic artifacts have characteristics that are image independent, facilitating their removal through dampening (via image denoising), and obtaining the maximum likelihood solution. In contrast with existing methods, such as compressed sensing, the fractal sampling is based on digital periodic lines that form the basis of discrete projected views of the image without requiring additional transform domains. This allows the creation of finite iterative reconstruction schemes in recovering an image from its fractal sampling that is also new to discrete tomography. As a result, ChaoS supports linear measurement and optimization strategies, while remaining capable of recovering a theoretically exact representation of the image. We apply the method to the simulated and experimental limited magnetic resonance (MR) imaging data, where restrictions imposed by MR physics typically favor linear measurements for reducing acquisition time.
- compressed sensing
- discrete Fourier slice theorem
- Fractal sampling
- missing data
- sparse image reconstruction