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We develop a maximum likelihood (ML)-based parametric image deconvolution technique to locate quantum-dot (q-dot) encoded microparticles from three-dimensional (3-D) images of an ultra-high density 3-D microarray. A potential application of the proposed microarray imaging is assay analysis of gene, protein, antigen, and antibody targets. This imaging is performed using a wide-field fluorescence microscope. We first describe our problem of interest and the pertinent measurement model by assuming additive Gaussian noise. We use a 3-D Gaussian point-spread-function (PSF) model to represent the blurring of the widefield microscope system. We employ parametric spheres to represent the light intensity profiles of the q-dot-encoded microparticles. We then develop the estimation algorithm for the single-sphere-object image assuming that the microscope PSF is totally unknown. The algorithm is tested numerically and compared with the analytical Cramer-Rao bounds (CRB). To apply our analysis to real data, we first segment a section of the blurred 3-D image of the multiple microparticles using a k-means clustering algorithm, obtaining 3-D images of single-sphere-objects. Then, we process each of these images using our proposed estimation technique. In the numerical examples, our method outperforms the blind deconvolution (BD) algorithms in high signal-to-noise ratio (SNR) images. For the case of real data, our method and the BD-based methods perform similarly for the well-separated microparticle images.