In some medical imaging applications, ultrasound images are strongly affected by speckle noise, generated by random constructive and destructive interference between ultrasound waves. Estimating a speckle-free ultrasound image, known as despeckling in the related literature, is an appealing and challenging task. This paper introduces a new concept of constructing an adaptive basis based on the principles of the quantum many-body interactive theory. This basis acts as a filter within the proposed speckle noise removal algorithm. Borrowing the idea of interaction from quantum mechanics, we introduce the concept of patch similarity in the formalism of despeckling. The proposed adaptive filter is tested on ultrasound images acquired from healthy and cancerous thyroids to illustrate its potential. The results show that the proposed method achieves a better compromise between contrast and resolution than two existing approaches.