Ionosphere has an important role in long distance HF communications, satellite communications and global navigation systems. Ionosphere is a plasma medium which arises due to solar and cosmic radiation, and the amount of ionization is highly time and location dependent. Eventually, the current state of the ionosphere should be continuously monitored with high accuracy. Total Electron Content (TEC) maps are being used to investigate the state of the ionosphere. There are online services which provide TEC maps, however they mostly have low spatial and temporal resolution and the techniques used for generating these maps are generally not accessible. TEC maps can also be generated from GNSS/GPS based Continuously Operating Receiver Stations (CORS) network measurements. Unfortunately, the GNSS/GPS receiver networks are not dense enough to form a map directly. Therefore, an algorithm should be used to estimate the TEC values at coordinates without a receiver. Based on the observation that TEC maps possess a high degree of sparsity, we propose a modified compressive sensing technique for generating regional TEC maps by using the sparse dataset obtained from a CORS network. We evaluate the performance of the proposed technique both over synthetically generated TEC maps which mimic the common characteristics of the ionosphere, and also over actual measurements taken over the Turkish National Permanent GPS Network (TNPGN) Active. Our analysis reveals that the proposed technique can produce TEC maps with high accuracy and resolution. We also demonstrate the superiority of our technique over other TEC map generation techniques found in the literature.