Two-stage Geometric Information Guided Image Reconstruction
This work addresses image reconstruction in compressive sensing for applications like medical imaging, though it appears incremental as it builds on existing methods like shearlet transforms and weighted TV.
The authors tackled the challenge of reconstructing high-quality images from very few noisy linear projections, particularly for piecewise smooth images like natural and medical images, by proposing a two-stage method called GeoCS that efficiently generates high-quality images.
In compressive sensing, it is challenging to reconstruct image of high quality from very few noisy linear projections. Existing methods mostly work well on piecewise constant images but not so well on piecewise smooth images such as natural images, medical images that contain a lot of details. We propose a two-stage method called GeoCS to recover images with rich geometric information from very limited amount of noisy measurements. The method adopts the shearlet transform that is mathematically proven to be optimal in sparsely representing images containing anisotropic features such as edges, corners, spikes etc. It also uses the weighted total variation (TV) sparsity with spatially variant weights to preserve sharp edges but to reduce the staircase effects of TV. Geometric information extracted from the results of stage I serves as an initial prior for stage II which alternates image reconstruction and geometric information update in a mutually beneficial way. GeoCS has been tested on incomplete spectral Fourier samples. It is applicable to other types of measurements as well. Experimental results on various complicated images show that GeoCS is efficient and generates high-quality images.