2016 Volume 34 Issue 4 Pages 177-185
High-dimensional data can be represented as a concise combination of explanatory data ingredients, which is referred to as the nature of sparsity. Compressed sensing is a general paradigm of sparsity-aware data acquisition to improve the functionality and lower the cost of measurement. For the compressed sensing fundamentally formulated as an underdetermined system of linear equations having a sparse solution, there have been provided theoretical underpinnings of random measurement and sparse reconstruction, as well as efficient sparse solvers based on convex relaxation. In imaging applications, reconstructed images are supposed to have sparse features, e.g., edges of objects. One can consistently derive practical algorithms for such image reconstruction by posing it as a linearly constrained convex optimization problem.
