Lu Gan, Thong Do, Trac Tran that seem to provide us with a compact measurement matrix with Fast compressive imaging using scrambled block Hadamard ensemble
The conclusion is attractive where one would to implement it right away:
With the advent of a single-pixel camera, compressive imaging applications have gained wide interests. However, the design of efficient measurement basis in such a system remains as a challenging problem. In this paper, we propose a highly sparse and fast sampling operator based on the scrambled block Hadamard ensemble. Despite its simplicity, the proposed measurement operator offers universality and requires a near-optimal number of samples for perfect reconstruction. Moreover, it can be easily implemented in the optical domain thanks to its integer-valued elements. Several numerical experiments show that its imaging performance is comparable to that of the dense, floating-coefficient scrambled Fourier ensemble at much lower implementation cost.
This paper has proposed the scrambled block Hadamard ensemble (SBHE) as a new sampling operator for compressive imaging applications. The SBHE is highly sparse and fast computable along with optical-domain friendly implementations. Both theoretical analysis and numerical simulation results have been presented to demonstrate the promising potential of the SBHE. In particular, we showed that a highly sparse SBHE can produce similar compressive imaging performance as that of a dense scrambled Fourier ensemble at much lower implementation cost.
In a different area Jianwei Ma provides a new fascinating reason for using Compressed Sensing in Compressed sensing for surface metrology.
Surface metrology is the science of measuring small-scale features on surfaces. In this paper we introduce compressed sensing theory into the surface metrology to reduce data acquisition. We describe that the compressed sensing is naturally fit to surface analysis. A recovery algorithm is proposed for scratched and textural surfaces by solving a convex optimal problem with sparse constrained by curvelet transform and wave atom transform. One can stably recover compressible surfaces from a random incomplete and inaccurate measurements, i.e., far fewer measurements than traditional methods use while does not obey the Shannon sampling theorem. This is very significant for measurements limited by physical and physiological constraints, or extremely expensive. The compressed measurement essentially shift measurement cost to computational cost of off-line nonlinear recovery. Thus we call this method as compressed metrology or computational metrology. Different from traditional measuring method, it directly senses the geometric and structural features instead of single pixel's information. By combining the idea of sampling, sparsity and compression, the compressed measurement indicates an new acquisition protocol and leads to building simpler and cheaper measurement instruments. Experiments on engineering and bioengineering surfaces demonstrate good performances of the proposed method.
Creidt Photo: Darvaza flaming crater in Turkmenistan John Bradley pictures, Via Fogonazos.