Rydberg-based Direction-of-Arrival (DoA) estimation has been hampered by the complexity of receiver arrays and the single-target, narrow-band limitations of existing single-receiver methods. This paper introduces a novel approach that addresses these limitations. We demonstrate that by spatially resolving the fluorescence profile along the vapor cell, the multi-target problem can be effectively solved. Our approach hinges on the insight that by superimposing incoming signals with a strong local oscillator (LO), the complex atomic absorption pattern is linearized into a simple superposition of sinusoids. In this new representation, each spatial frequency uniquely and directly maps to the DoA of a target. This reduces the multi-target challenge into a spectral estimation problem, which we address using Prony's method. Our approach, termed Imaging-based Spectral Estimation (ISE), inherently supports multi-target detection and restores the full broadband capability of the sensor by removing the restrictive cell-length dependency. This development also shows potential for realizing multi-channel Rydberg receivers and the continuous-aperture sensing required for holographic multiple-input multiple-output (MIMO). We develop a comprehensive theoretical model, derive the Cramer-Rao Lower Bound (CRLB) as a performance benchmark, and present simulations validating the effectiveness of the approach to resolve multiple targets.