An algorithm based on the Haar wavelet basis and implementing an expectation maximization-maximum penalized likelihood estimator in 3-D is shown to provide dramatic improvement over traditional stopped-EM algorithms in terms of mean-squared error on simulated data for confocal microscopy systems. Confocal microscopy is one of many modern medical imaging systems changing the landscape of medical research and practice, and the blurred and grainy images produced are much more useful when suitable, accurate reconstruction algorithms are applied. The industry standard, the stopped expectation-maximization algorithm proves unreliable and inadequate when compared to penalized likelihood estimators based on spatially adaptive bases such as wavelets. In addition, processing confocal microscopy images in 3-D, rather than slice-wise in 2-D, takes into account the blurring that occurs between slices as a result of the microscope's point spread function.