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This paper proposes a general framework for compressed sensing of constrainedjoint sparsity (CJS) which includes total variation minimization (TV-min) as anexample. TV- and 2-norm error bounds, independent of the ambient dimension, arederived for the CJS version of Basis Pursuit and Orthogonal Matching Pursuit.As an application the results extend Cand`es, Romberg and Tao's proof of exactrecovery of piecewise constant objects with noiseless incomplete Fourier datato the case of noisy data.

TV-min and Greedy Pursuit for Constrained Joint Sparsity and Application to Inverse Scattering