Ill-posed problems arise in many image processing applications, including microscopy, medicine and astronomy. Iterative methods are typically recommended for these large scale problems, but they can be difficult to use in practice. For example, enforcing nonnegativity constraints can be expensive. In this talk we consider a class of efficient nonnegatively constrained iterative algorithms that are derived from the noise statistics of the image formation process, and show that these can be interpreted as covariance preconditioned steepest descent methods. Image processing examples are used to illustrate concepts and to test and compare algorithms.