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We present a data-driven, project-based algorithm which enhances image resolution by extrapolating high-band wavelet coefficients. High-resolution images are reconstructed by alternating the projections onto two constraint sets: the observation constraint defined by the given low-resolution image and the prior constraint derived from the training data at the high resolution (HR). Two types of prior constraints are considered: spatially homogeneous constraint suitable for texture images and patch-based inhomogeneous one for generic images. A probabilistic fusion strategy is developed for combining reconstructed HR patches when overlapping (redundancy) is present. It is argued that objective fidelity measure is important to evaluate the performance of resolution enhancement techniques and the role of antialiasing filter should be properly addressed. Experimental results are reported to show that our projection-based approach can achieve both good subjective and objective performance especially for the class of texture images.