## 1 Introduction  
Cement is one of the most widely used materials in construction due to its versatility, strength, and durability. Furthermore, as a primary component of concrete and mortar, it plays a critical role in the development of building structures. Its workability and ability to harden and gain strength over time makes it indispensable for creating long-lasting and resilient structures, ensuring its continued importance in the construction industry around the world. However, cement-based materials are exposed to a variety of physical and chemical disturbances that could affect their properties during their service life. These disturbances often induce some kind of deterioration, which manifests itself as external or internal pathologies, ultimately compromising the material's mechanical properties. Among the numerous damage mechanisms affecting cementitious materials, gradient damage processes are particularly significant [1; 2] and arise from variations in temperature, humidity, or chemical reactions within the material. Notably, these deterioration processes typically propagate from the exterior towards the interior of the material and can be broadly categorized into chemical types (e.g., external sulfate, acid attacks, and carbonation) and physical types (e.g., high-temperature exposure). In the context of physical damage, high-temperature exposure alters the hydration products of cement [3], producing microcracks within the matrix and at the aggregate-matrix interface. These alterations reduce their mechanical properties such as compressive strength, hardness, and elastic modulus. In the context of chemical attacks, carbonation is a natural chemical reaction which occurs when carbon dioxide (CO\({}_{2}\)) in the air reacts with hydrated cement compounds, forming calcium carbonate (CaCO\({}_{3}\)). The formation of calcium carbonate produces a densification (reduction in porosity) of the cementing matrix and creates a pH gradient [4]. The pH reduction undermines the passive layer protecting the embedded steel reinforcement, exposing it to corrosion in the presence of moisture and oxygen. Taking this into consideration, the corrosion products, predominantly rust, occupy a larger volume than the original steel, causing internal stress that results in cracking, spalling, and a significant decrease in structural integrity. This interplay of physical and chemical disturbances underlines the necessity of understanding and estimating the gradient damage in order to enhance the durability and performance of cement-based materials. Previous studies on non-destructive testing have extensively utilized ultrasonic techniques to detect and evaluate damage in concrete arising from this type of pathology. Moreover, these studies predominantly employed ultrasonic velocity as a diagnostic parameter to determine the differences between damaged and undamaged samples. For example, in [5], the carbonate front was successfully estimated using Quantitative Ultrasound Imaging (QUS) with high-frequency ultrasound signals (2.5 MHz). This method leverages an array of transducers and the analysis of microstructural information through backscattering and attenuation coefficients. Another approach to identifying damaged regions involves ultrasonic tomography, which irradiates the specimen from multiple positions [6]. The collected signals form projections, which enable the generation of visual cross-sectional images of the material using reconstruction algorithms, all without causing any damage. Since its beginnings, tomography has played a crucial role in quality control and is used in multiple disciplines such as medicine, archaeology, biology, geophysics, oceanography, and science, among other disciplines. Tomographic reconstruction algorithms can be categorized into three primary groups: transformed, algebraic, and machine-learning-based techniques. Transformed algorithms reconstruct images by applying the Fourier Slice Theorem [7] to projections.