JPEG is the most used image compression algorithm but block wise DCT compression methods produce artifacts due to coefficient quantization. JPEG decompression can be seen as a reconstruction problem constrained by quantization. In this context, we propose to handle this problem by using interval-valued arithmetic. Our method allows to produce interval-valued image that includes the non-compressed original image. The produced convex set allows to apply constrained Total Variation (TV) reconstruction in order to reduce JPEG artifacts (blocking, grainy effects and high frequency noise). Experiments show visual improvement of JPEG decoding assessed by non-reference quality metric. In addition, the stopping criterion of the TV algorithm is given by this metric which provides evidence about JPEG decompression improvement.