Image processing algorithms continue to demand higher performance from computers. However, computer performance is not improving at the same rate as before. In response to the current challenges in enhancing computing performance, a wave of new technologies and computing paradigms is surfacing. Among these, memristors stand out as one of the most promising components due to their technological prospects and low power consumption. With efficient data storage capabilities and their ability to directly perform logical operations within the memory, they are well-suited for in-memory computation (IMC). Approximate computing emerges as another promising paradigm, offering improved performance metrics, notably speed. The tradeoff for this gain is the reduction of accuracy. In this article, we are using the stateful logic material implication (IMPLY) in the semi-serial topology and combine both the paradigms to further enhance the computational performance. We present three novel approximated adders that drastically improve speed and energy consumption with an normalized mean error distance (NMED) lower than 0.02 for most scenarios. We evaluated partially approximated Ripple carry adder (RCA) at the circuit-level and compared them to the State-of-the-Art (SoA). The proposed adders are applied in different image processing applications and the quality metrics are calculated. While maintaining acceptable quality, our approach achieves significant energy savings of 6%–38% and reduces the delay (number of computation cycles) by 5%–35%, demonstrating notable efficiency compared to exact calculations.

As the demand for computational power increases drastically, traditional solutions to address those needs struggle to keep up. Consequently, there has been a proliferation of alternative computing paradigms aimed at tackling this disparity. Approximate Computing (AxC) has emerged as a modern way of improving speed, area efficiency, and energy consumption in error-resilient applications such as image processing or machine learning. The trade-off for these enhancements is the loss in accuracy. From a technology point of view, memristors have garnered significant attention due to their low power consumption and inherent non-volatility that makes them suitable for In-Memory Computation (IMC). Another computing paradigm that has risen to tackle the aforementioned disparity between the demand growth and performance improvement. In this work, we leverage a memristive stateful in-memory logic, namely Material Implication (IMPLY). We investigate advanced adder topologies within the context of AxC, aiming to combine the strengths of both of these novel computing paradigms. We present two approximated algorithms for each IMPLY based adder topology. When embedded in an Ripple Carry Adder (RCA), they reduce the number of steps by$6\%-54\%$and the energy consumption by$7\%-54\%$compared to the corresponding exact full adders. We compare our work to State-of-the-Art (SoA) approximations at circuit-level, which improves the speed and energy efficiency by up to$72\%$and$34\%$, while lowering the Normalized Median Error Distance (NMED) by up to$81\%$. We evaluate our adders in four common image processing applications, for which we introduce two new test datasets as well. When applied to image processing, our proposed adders can reduce the number of steps by up to$60\%$and the energy consumption by up to$57\%$, while also improving the quality metrics over the SoA in most cases.