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Existing algorithmsare generally denouncing the existence of clusters with large amplitude coefficients. The L1 norm as well as other distinct models of sparsity does not attract a cluster tendency (group sparsity). In the light of a minimisation of convex cost work fusing the blended norm, this work introduces the technique "overlapping group shrinking." The groups are completely overlapping in order to abstain from blocking relics. A basic minimization calculation, in light of progressive replacement, is inferred. A straightforward strategy for setting the regularization boundary, in view of constricting the noise to a predefined level, is portrayed in detail by combining OGS with one of the most powerful mathematical tool wavelet transforms. In fact, the CWT coefficients are processed by OGS to produce a noise-free signal. The CWT coefficients are also processed.The proposed approach is represented on MST RADAR signals, the denoised signals delivered by CWT combined with OGS are liberated from noise.