The proliferation of digital cameras, wireless networks and distributed computing make sharing of visual data easier than ever. Such casual exchange of data, however, has increasingly raised questions on how sensitive visual information can be protected. Encrypted-domain signal processing techniques based on homomorphic encryption and garbled circuits are increasingly applied for such applications. Their high computation and communication complexity, however, are not suitable for pixel-level processing. In this paper, we propose an alternative approach of using information-theoretically secure protocols over multiple non-colluding semi-honest computing agents. The proposed protocols are based on classical Shamir's secret sharing scheme which supports multiplication and addition in the random-share domain. We extend the sharing scheme to handle other fundamental signal processing operations and use them to develop a novel privacy-protected wavelet denoising scheme over three computing agents. Our experimental results demonstrate the viability of using information-theoretic secure protocols to safeguard privacy in distributed pixel-level processing.