Sparse arrays reduce the number of active channels that effectively increases the inter-element spacing. Large inter-element spacing results in grating lobe artifacts degrading the ultrasound image quality and reducing the contrast-to-noise ratio. A deep learning-based custom algorithm is proposed to estimate inactive channel data in periodic sparse arrays. The algorithm uses data from multiple active channels to estimate inactive channels. The estimated inactive channel data effectively reduces the inter-element spacing for beamforming, thus suppressing the grating lobes. Estimated inactive element channel data was combined with active element channel data resulting in a pseudo fully sampled array. The channel data was beamformed using a simple delay-and-sum method and compared with the sparse array and fully sampled array. The performance of the algorithm was validated using a wire target in a water tank, multi-purpose tissue-mimicking phantom, and carotid data. Grating lobes suppression up to 15.25 dB was observed with an increase in contrast-to-noise (CNR) for the pseudo fully sampled array. Hypoechoic regions showed more improvement in CNR than hyperechoic regions. Root-mean-square error for unwrapped phase between fully sampled array and the pseudo fully sampled array was low, making the estimated data suitable for Doppler and elastography applications. Speckle pattern was also preserved; thus, the estimated data can also be used for quantitative ultrasound applications. The algorithm can improve the quality of sparse array images and has applications in small scale ultrasound devices and 2D arrays.