We present a new iterative quantization procedure for oversampled frames with guaranteed convergence and stability. The procedure uses similar concepts to that of turbo decoding in the context of error control coding. The quantization process is modeled as a quadratic integer-programming problem. A trellis structure is introduced to solve the problem, where the quantized coefficients represent a path through the trellis diagram. The quantization metric is iteratively improved through turbo iterations by exchanging quantization extrinsic information. The proposed procedure is shown to provide significant improvement over prior art in quantization and integer programming.