We propose a denoising method for digital holography mod 2π wrapped phase map by using an adaptation of the SPArsity DEnoising of Digital Holograms (SPADEDH) algorithm. SPADEDH is a l(1) minimization algorithm able to suppress the noise components on digital holograms without any prior knowledge or estimation about the statistics of noise. We test our algorithm with either general numerical simulated wrapped phase, quantifying the performance with different efficiency parameters and comparing it with two popular denoising strategies, i.e., median and Gaussian filters, and specific experimental tests, by focusing our attention on long-sequence wrapped quantitative phase maps (QPMs) of in vitro cells, which aim to have uncorrupted QPMs. In addition, we prove that the proposed algorithm can be used as a helper for the typical local phase unwrapping algorithms.