A New Reconstruction Approach to Compressed Sensing

Compressed sensing is a new concept in signal processing where one seeks to minimize the number of measurements to be taken from signals while still retaining the information necessary to approximate them well. Nonlinear algorithms, such as l₁ norm optimization problem, are used to reconstruct the signal from the measured data. This paper proposes a maximum entropy function method which intimately relates to homotopy method as a computational approach to solve the l₁ optimization problem. Maximum entropy function method makes it possible to design random measurements which contain the information necessary to reconstruct signal with accuracy. Both the theoretical evidences and the extensive experiments show that it is an effective technique for signal reconstruction. This approach offers several advantages over other methods, including scalability and robustness.