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Existing image codec technologies are based on transform which make image signal can be compressed, while quantization has been used to control bit rates. Compressive sensing (CS), which is a novel signal processing and recovery method, can be applied to image decoding to replace inverse transform reconstruction. This paper proposes an error estimate method based on equalization quantization noise model for image codec. Due to the robust character of CS, it can upgrade the quality of reconstruction when error has been estimated accurately. With designed equalization matrix, a new norm constraint which can enhance the quality of CS recovery significantly has been shown. A CS-based JPEG decoding scheme based on quantization error estimate is also presented, and experimental evidence exhibits more gains over CS reconstruction without error estimation and original JPEG decoder.