The paper analyses the possibility to recover different biomedical signals if limited number of samples is available. Having in mind that monitoring of health condition is done by measuring and observing key parameters such as heart activity through electrocardiogram or anatomy and body processes through magnetic resonance imaging, it is important to keep the quality of the reconstructed signal as better as possible. To recover the signal from limited set of available coefficients, the Compressive Sensing approach and optimization algorithms are used. The theory is verified by the experimental results.