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Estimation of mechanical structure damage can greatly benefit from the knowledge that the damage accumulates irreversibly over time. This paper formulates a problem of estimation of a pixel-wise monotonic increasing (or decreasing) time series of images from noisy blurred image data. Our formulation includes temporal monotonicity constraints and a spatial regularization penalty. We cast the estimation problem as a large-scale quadratic programming (QP) optimization and describe an efficient interior-point method for solving this problem. The method exploits the special structure of the QP and scales well to problems with more than a million of decision variables and constraints. The proposed estimation approach performs well for simulated data. We demonstrate an application of the approach to diagnostic images obtained in structural health monitoring experiments and show that it provides a good estimate of the damage accumulation trend while suppressing spatial and temporal noises.