Micro-motion dynamics and geometrical shape are considered to be essential evidence for infrared (IR) ballistic target recognition. However, it is usually hard or even impossible to describe the geometrical shape of an unknown target with a finite number of parameters, which results in a very difficult task to estimate target micro-motion parameters from the IR signals. Considering the shapes of ballistic targets are relatively simple, this paper explores a joint optimization technique to estimate micro-motion and dominant geometrical shape parameters from sparse decomposition representation of IR irradiance intensity signatures. By dividing an observed target surface into a number of segmented patches, an IR signature of the target can be approximately modeled as a linear combination of the observation IR signatures from the dominant segmented patches. Given this, a sparse decomposition representation of the IR signature is established with the dictionary elements defined as each segmented patch's IR signature. Then, an iterative optimization method, based on the batch second-order gradient descent algorithm, is proposed to jointly estimate target micro-motion and geometrical shape parameters. Experimental results demonstrate that the micro-motion and geometrical shape parameters can be effectively estimated using the proposed method, when the noise of the IR signature is in an acceptable level, for example, SNR>0 dB.