The use of concrete structures has made its long-term performance crucial for the safe operation of commercial nuclear power plants (NPPs), especially with license period extensions to sixty years and possibly beyond. Unlike most metallic materials, reinforced concrete used in NPPs is a heterogeneous material, a composite with a low-density matrix, a mixture of cement, sand, aggregate and water, and a high-density reinforcement, made up of steel rebar or tendons. This structural complexity makes nondestructive evaluation (NDE) a challenging task. While the standard Synthetic Aperture Focusing Technique (SAFT) is adequate for many defects with shallow concrete cover, some defects that are located under deep concrete cover are not easily identified using the standard SAFT techniques. For many degradation mechanisms, particularly defects under deep cover, the use of advanced signal processing techniques is required. A variety of test specimens were evaluated using several advanced signal processing techniques ranging from a large specimen representative of a NPP containment wall (2.134 m x 2.134 m x 1.016 m) with twenty embedded defects, to specimens with accelerated alkali-silica reaction (ASR), and specimens with freeze-thaw damage. The first technique examined in this paper generates frequency banded SAFT reconstructions using wavelet packet decomposition and reconstruction. While the frequency banded SAFT reconstructions show a vast improvement over the standard SAFT for defects under deep cover, a second technique, Model Based Iterative Reconstruction (MBIR), has been initiated to address the limitations of the frequency banded SAFT (such as multiple reflections for a single defect).