The ill-posed inverse problem of image restoration is studied. Firstly, the mathematical model and ill-posed property of image restoration are analyzed, and a Fourier-curvelet combined image restoration (ForCurIR) algorithm is proposed. ForCurIR algorithm exploits the Fourier transform’s sparse representation of the colored noise and curvelet transform’s sparse representation piecewise smooth images. The problem of image restoration is turned into constrained deconvolution in Fourier domain and constrained denoising in curvelet domain. Deconvolution and noise suppressing are performed via shrinkage both in the Fourier and curvelet domain. Experimental results demonstrate that ForCurIR algorithm can properly retrieve various kinds of image edges, and the signal-to-noise ratio (SNR) and visual quality of the restored images are improved significantly.