In the large body of research literature on image restoration, very few papers were concerned with compression-induced degradations, although in practice, the most common cause of image degradation is compression. This paper presents a novel approach to restoring JPEG-compressed images. The main innovation is in the approach of exploiting residual redundancies of JPEG code streams and sparsity properties of latent images. The restoration is a sparse coding process carried out jointly in the DCT and pixel domains. The prowess of the proposed approach is directly restoring DCT coefficients of the latent image to prevent the spreading of quantization errors into the pixel domain, and at the same time, using online machine-learned local spatial features to regulate the solution of the underlying inverse problem. Experimental results are encouraging and show the promise of the new approach in significantly improving the quality of DCT-coded images.