A sparsity-exploiting algorithm intended for few-view single photon emission computed tomography (SPECT) reconstruction is proposed and characterized. The algorithm models the object as piecewise constant subject to a blurring operation. To validate that the algorithm closely approximates the true object in the noiseless case, projection data were generated from an object assuming this model and using the system matrix. Monte Carlo simulations were performed to provide more realistic data of a phantom with varying smoothness across the field of view and a cardiac phantom. Reconstructions were performed across a sweep of two primary design parameters. The results demonstrate that the algorithm recovers the object in a noiseless simulation case. While the algorithm assumes a specific blurring model, the results suggest that the algorithm may provide high reconstruction accuracy even when the object does not match the assumed blurring model. Generally, increased values of the blurring parameter and total variation weighting parameters reduced streaking artifacts, while decreasing spatial resolution. The proposed algorithm demonstrated higher correlation with respect to the true phantom compared to maximum-likelihood expectation maximization (MLEM) reconstructions. Images reconstructed with the proposed algorithm demonstrated reduced streaking artifacts when reconstructing from few views compared to MLEM. The proposed algorithm introduced patchy artifacts in some reconstructed images, depending on the noise level and the selected algorithm parameters. Overall, the results demonstrate preliminary feasibility of a sparsity-exploiting reconstruction algorithm which may be beneficial for few-view SPECT.