  A measurement of the transverse momentum spectra of jets in Pb-Pb collisions
at $\sqrt{s_{\rm NN}}=2.76$ TeV is reported. Jets are reconstructed from
charged particles using the anti-$k_{\rm T}$ jet algorithm with jet resolution
parameters $R$ of $0.2$ and $0.3$ in pseudo-rapidity $|\eta|<0.5$. The
transverse momentum $p_{\rm T}$ of charged particles is measured down to $0.15$
GeV/$c$ which gives access to the low $p_{\rm T}$ fragments of the jet. Jets
found in heavy-ion collisions are corrected event-by-event for average
background density and on an inclusive basis (via unfolding) for residual
background fluctuations and detector effects. A strong suppression of jet
production in central events with respect to peripheral events is observed. The
suppression is found to be similar to the suppression of charged hadrons, which
suggests that substantial energy is radiated at angles larger than the jet
resolution parameter $R=0.3$ considered in the analysis. The fragmentation bias
introduced by selecting jets with a high $p_{\rm T}$ leading particle, which
rejects jets with a soft fragmentation pattern, has a similar effect on the jet
yield for central and peripheral events. The ratio of jet spectra with $R=0.2$
and $R=0.3$ is found to be similar in Pb-Pb and simulated PYTHIA pp events,
indicating no strong broadening of the radial jet structure in the
reconstructed jets with $R<0.3$.
