This paper presents a lossy compression scheme for biomedical images by using a new method. Image data compression using Vector Quantization (VQ) has received a lot of attention because of its simplicity and adaptability. VQ requires the input image to be processed as vectors or blocks of image pixels. The Finite-state vector quantization (FSVQ) is known to give better performance than the memory less vector quantization (VQ). This paper presents a novel combining technique for image compression based on the Hierarchical Finite State Vector Quantization (HFSVQ) and the neural network. The algorithm performs nonlinear restoration of diffraction-limited images concurrently with quantization. The neural network is trained on image pairs consisting of a lossless compression named hierarchical vector quantization. Simulations results are presented that demonstrate improvements in visual quality and peak signal-to-noise ratio of the restored images.