Signal reconstruction after compressed sensing using probabilistic approximation and gradient descent

Compressed sensing allows for signal sampling at frequencies much lesser than the Nyquist rate, thus allowing for lesser resource and area consumption of sampling modules as well as lesser data rates for information transfer. However the process of signal reconstruction is based on constraints of sparsity and requires methods more complex than sinc interpolation, which is used in Nyquist sampled reconstruction. Some of the methods used are l1 norm minimisation, convex optimisation as well as greedy methods. This paper describes a reconstruction algorithm using probabilistic approximation and gradient descent. Satisfactory results have been obtained and this concept can be further developed and optimised for large scale usage.