High-resolution observations of protoplanetary disks with radio interferometers are crucial for understanding the planet formation process. Recent observations using Atacama Large Millimeter/submillimeter Array (ALMA) have revealed various small-scale structures in disks. In interferometric observations, the observed data are an incomplete set of Fourier components of the radio source image. The image reconstruction is therefore essential in obtaining the images in real space. The CLEAN technique has been widely used, but recently, a new technique using the sparse modeling approach is suggested. This technique directly solves a set of undetermined equations and has been shown to behave better than the CLEAN technique based on mock observations with VLBI (Very Long Baseline Interferometry). However, it has never been applied to ALMA-like connected interferometers nor real observational data. In this work, for the first time, the sparse modeling technique is applied to observational data sets taken by ALMA. We evaluate the performance of the technique by comparing the resulting images with those derived by the CLEAN technique. We use two sets of ALMA archival data at Band 7 ($\sim$350 GHz) for the protoplanetary disk around HD 142527. One is taken in the intermediate-baseline array configuration, and the other is in the longer-baseline array configuration. The image resolutions reconstructed from these data sets are different by a factor of $\sim$ 3. We compare images reconstructed using sparse modeling and CLEAN. We find that the sparse modeling technique can successfully reconstruct the overall disk emission. The previously known disk structures appear on both images made by the sparse modeling and CLEAN at its nominal resolutions. Remarkably, the image reconstructed from intermediate-baseline data using the sparse modeling technique matches very well with that obtained from longer-baseline data using the CLEAN technique.