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The reliability and security of convolutional neural networks (CNNs) have attracted growing attention, particularly in domains where safety is paramount, such as clinical medicine. Even though CNNs demonstrate high competency in categorizing images, their outcomes frequently exhibit vulnerability to minor image adjustments that remain imperceptible to human observers. Consequently, an altered, degraded image can appear identical to the authentic image to a person, yet mislead the CNN into making an incorrect classification. Throughout this study, these altered images are termed adversarial images. A widespread approach for producing adversarial images involves propagating the loss gradient backward to alter the source image. Typically, perturbations have been established using solely the gradient direction and a fixed step size (referred to as the fast gradient sign method, or FGSM), or by executing the FGSM iteratively to craft more potent perturbations capable of altering the model's categorization (i-FGSM). Conversely, if the step size is excessively large, the smallest possible image perturbation might be overlooked during the gradient exploration. To discover precise and minimal input image variations necessary to prompt a classification shift, this paper proposes initiating the FGSM with a small step size and dynamically tuning it across iterations. For evaluation, several decay algorithms from existing literature were assessed against a novel method driven by an index monitoring the state of the loss. Ultimately, three separate tracking functions were implemented for comparative analysis. The empirical findings demonstrate that our loss-adaptive decay algorithms successfully identified adversarial examples with a success rate exceeding 90% while introducing fewer distortions to mislead the CNNs.