The inspirals of stellar-mass compact objects into supermassive black holes are some of the most exciting sources of gravitational waves for LISA. Detection of these sources using fully coherent matched filtering is computationally intractable, so alternative approaches are required. In , we proposed a detection method based on searching for significant deviation of power density from noise in a time-frequency spectrogram of the LISA data. The performance of the algorithm was assessed in  using Monte-Carlo simulations on several trial waveforms and approximations to the noise statistics. We found that typical extreme mass ratio inspirals (EMRIs) could be detected at distances of up to 1-3 Gpc, depending on the source parameters. In this paper, we first give an overview of our previous work in [1, 2], and discuss the performance of the method in a broad sense. We then introduce a decomposition method for LISA data that decodes LISA's directional sensitivity. This decomposition method could be used to improve the detection efficiency, to extract the source waveform, and to help solve the source confusion problem. Our approach to constraining EMRI parameters using the output from the time-frequency method will be outlined.