Compressive sensing least square problem solution suitable for implementation

Compressive Sensing approach allows reconstruction of under-sampled sparse signals, by using different optimization techniques. These techniques solve undetermined systems of equations which may be recast as least square problems. Since there is a growing need for real-time hardware implementations of the reconstruction methods, it is important for these methods to be fast enough and not be computationally demanding. Here, we will focus on QR decomposition based approach for solving least square problems. Least square problem solution is defined in such way that does not require Q matrix, obtained as a result of QR decomposition of the measurement matrix, to be used in calculation and leads to the lower computational complexity.