Approximate computing has become a widely recognized method for designing energy-efficient arithmetic architectures in the context of error-tolerant applications. This paper presents the design and analysis of a 4-bit approximate Vedic multiplier (AVMT) using the Urdhva Tiryagbhyam method. This Vedic approach, involving vertical and crosswise steps, outperforms traditional multiplication in terms of efficiency. An approximate 2-bit multiplier (AVM2) is designed, and an AVMT is proposed using AVM2. The proposed architecture has better propagation delay and less area utilization compared to other conventional multipliers. AVMT has an 11% reduction in area consumption and a 12% increase in processing speed compared to the exact Vedic multiplier. To assess its practicality in real-world scenarios, the proposed multiplier is integrated into an image-blending application. The results indicate that the system achieves a Structural Similarity Index (SSIM) average value of 0.91, which proves to be suitable for error-resilient image processing applications.