Geometric structure guided collaborative compressed sensing

• A geometric structure guided collaborative reconstruction method.
• A hybrid use of the geometric structure and self-similarity property of images.
• Geometric structure estimation on compressed measurements.
• Structured sparse models related to geometric structures.

Employing overcomplete dictionaries for applications captures the great interest, but the problem of recovering a signal from its random compressed measurements by taking advantage of the sparsity prior introduced by an overcomplete dictionary is very ill-posed, due to the compressed sampling operator and the redundancy of the dictionary. To achieve accurate and stable estimation, we exploit the local geometric structures of an image, and make a hybrid use of them and the self-similarity property of natural images. In the proposed geometric structure guided collaborative compressed sensing reconstruction (GS_CR) method, the geometric structured sparsity models are established and imposed to the sparse representation coefficients of the image blocks, which are designed to enhance the estimation accuracy of the local structures of an image. In the two reconstruction processes of GS_CR, the collaborative reconstruction patterns adapted to the geometric structures are established, where an image block is estimated by the collaboration of its local and nonlocal neighbors of different geometric types. By the experimental results, GS_CR is shown to outperform the previously proposed collaborative reconstruction scheme in reconstruction accuracy and speed.